The Lost Uchiha
#01—Uchiha Sasuke x Ty Lee
Sasuke ends up in the Avatar world when the past Avatar's use Aang's pent up energy to open a split-second portal to pull Naruto to their world to help Aang survive. Because of the Kyuubi's influence, their pull was deflected away from him and they got Sasuke instead (when Sasuke 'dies' on the bridge at Haku's hands).
When he wakes up, Sasuke seeks a way to return back to his own world so he can finish his goal of avenging his family. With strong suspicions against him, Sasuke is forced to first leave the Water Tribe with Aang. Though strongly confused about the strange world he'd found himself in, Sasuke decides to accompany Aang on his journey to the North Pole because he figured that it would've been safer for him to travel with someone he knew and who was familiar with the world. It isn't until Aang's visit to the Fire Temple and his meeting with Roku that they learn the secret behind Sasuke's presence in the Avatar world. The only way for Sasuke to be returned to his homeworld is if Aang masters all four elements and gains complete control of the Avatar State. But by then, he had voluntarily gotten drawn into the Avatar's journey because he sees it as a training exercise.
With his new Sharingan and easy control of his chakra, Sasuke is able to copy and use all of the bending forms, though he usually prefers to fight with Firebending. Sasuke decides to not teach Aang how to bend the other elements because he doesn't see himself as a teacher and because although he knows how to use them, he doesn't understand the significance of certain principles that the bending forms rely on. However, Sasuke fights on the frontlines in all of the Avatar's major battles, most notably the Battle of the North Pole where he sunk several dozen ships singlehandedly. However, Sasuke's unique jutsu and abilities quickly garnered him a wanted status in the Fire Nation, even more so because he was a companion to the Avatar.
This is how he first fights Azula, Mai, and Ty Lee when they ambush them in Omashu. Sasuke and Azula quickly form a potent and deadly rivalry because of their shared status as Firebenders, prodigies, royalty status (even if it was figuratively for Sasuke), and superiority complexes. Though he respects her perfect aim and skill with bladed weapons, Sasuke finds no other outstanding interests in Mai. Yet it was Ty Lee who quickly drew his attention because of her pressure point fighting style, tremendous strength and agility, and disarming 'tease' personality. But as he fights against them more often, he finds himself becoming increasingly enamored by Ty Lee because of her prowess, beauty, and his emerging hormones. And Ty Lee frequently makes it a habit to flirt with the extremely cute 'ninja-boy'.
But Sasuke isn't the only ninja who was summoned to the Avatar world. Through the collaboration of several Dark Spirits, Mizuki also gets chosen but with full awareness of where he was going. (My original idea was for it to be Deidera, but I realized he was too powerful for Sasuke at that age and I couldn't think of any other ninja to take his place at the time) The Dark Spirits promised him tremendous power and strength in return for helping the Fire Nation conquer the world. It was a task that Mizuki happily agreed to because it allowed him to attack and destroy many people at his own desire. Mizuki wasted no time in allying himself to the Fire Lord and getting sent into the Earth Kingdom to break the wall of Ba Sing Se. Only through the combined efforts of Sasuke and Aang was Mizuki defeated and forced to retreat (along with ruining the Fire Nation's giant drill). Though surprised to find that there was another ninja of his type in the world, Mizuki and Sasuke both realize that they are on opposing sides of the field and begin to hunt one another. They finally meet in battle the same night that Zuko joins Azula and almost kill Aang. Sasuke was soundly defeated because he got arrogant and overestimated his abilities. If not for Appa arriving and Katara healing his wounds, Sasuke would've died.
After recovering from their fights and entering the Fire Nation, Sasuke is allowed by Sokka's sword master to make his own sword out of the meteorite they found earlier. With his new sword and an aspiring dueling partner, Sasuke and Sokka begin to work on their swordsmanship. During the Day of Black Sun, Sasuke is part of the main invasion battle and was responsible for the destruction of the first barrier of the Fire Nation and in destroying several other security barriers. But as the battle progresses, he becomes increasingly suspicious that something is wrong with the invasion plans. He quickly confides with the others that their plans had likely been discovered and countered. He is proven correct when the Fire Nation Air Force appears and destroys their submarines. The battle worsens for them when Mizuki appears and Sasuke gets drawn into a battle with him, distracting him while the others flee on Appa.
Captured by Mizuki, he is briefly interrogated before he and several others get transferred to the Boiling Rock. While there, he decides to wait and train, believing that eventually Aang and the others would come for him. He is proven right when Sokka and Zuko show up and they begin planning their escape. However, their escape plans are botched when Azula appears, desiring to interrogate Zuko and Sasuke personally. It isn't until they receive some surprising help from Mai and Ty Lee that they succeed in escaping. And it was after this escape that Sasuke realized that he was starting to develop feelings for Ty Lee because he constantly was finding himself worrying about her safety after her betrayal of Azula.
When Sozin's Comet finally appeared, Sasuke knew that he had only one opponent he needed to face in the coming battle: Mizuki. He guessed that Mizuki would likely be accompanying the Armada as an escort in case they ran into trouble. When Aang made his attack on Ozai's airship, Sasuke also finds and attacks Mizuki while Sokka, Suki, and Toph take out the Armada. After a long, climatic battle, Sasuke finally overcomes Mizuki. However, rather than submit to defeat, Mizuki commits suicide and attempts to destroy Sasuke along with him. If not for Aang's coincidental interruption during his battle with Ozai in his Avatar State, Sasuke would've been incinerated by the blast.
After Ozai's defeat, the freeing of Ba Sing Se, and Zuko's coronation as the Fire Lord, the group journeyed to Ba Sing Se to meet with the Earth King. While there, Sasuke finally confronts Ty Lee about his feelings and the truth about who he is and where he came from. He promises that, if he had a choice, he would happily stay with her. But because of his vow to his murdered family, Sasuke chooses to return back to his homeworld. Ty Lee gives him a small pendant to remember her by. After Aang taps into his new Avatar powers, he opens the portal to send Sasuke home.
When he awakens, Sasuke quickly realizes that no time had passed in his homeworld (he was still in Wave Country when he was 'killed' by Haku on the bridge). If not for pendant that Ty Lee had given him, Sasuke would've started believing that all that had happened to him had been nothing more than an elaborate dream induced by his near-death experience. Unknown to him, the Spirits of the Avatar world continued to watch over him as he continues his life in his own world.
After he kills Itachi three years later, Sasuke faints from exhaustion. When he reawakens, he once again finds himself back in the Avatar world, once again summoned by the Avatar Spirits. However, this time, he was summoned because the Spirits knew that he would never find true peace in his own world (even now that he'd completed his ambition) and they brought him back to help Aang and Zuko ease the tensions between the Four Nations as the wounds of war slowly healed. Sasuke would eventually find and marry Ty Lee, living as peaceful a life as he could.