Another reason could be that the gods are bored and want to see some chaos or interesting interactions. They know that Percy's arrival in the Avengers' world will stir things up. His powers and personality are so different from the Avengers that there will surely be some unexpected developments. It could also be part of a bigger plan to unite different heroic forces for a future event that the gods foresee.
Perhaps the gods see a threat that only Percy and the Avengers together can defeat. So they send Percy to team up with them.
It could be that the gods want Percy to gain new experiences and knowledge from the Avengers' world. The Avengers have a different way of handling threats and protecting the world, and the gods might think this exposure will make Percy a better hero in his own realm. Also, it might be a test for Percy. The gods are known for their tricky ways, and sending him to a new and different group like the Avengers could be a way to see how he adapts and overcomes challenges outside of his comfort zone.
In the fanfiction, Percy might have some culture clashes with the Avengers. He comes from a world of Greek gods, and the Avengers are from a more modern, superhero - based world. He could introduce them to new concepts like the power of the Olympian gods. For example, he might tell them about how the gods can interfere in human affairs, which could change the Avengers' perspective on their own battles. Also, his combat skills, which are different from the Avengers', could be a great addition to the team. He is used to fighting mythological creatures, so facing off against some of the Avengers' foes might be a new and exciting challenge for him.
Probably Poseidon, as he is Percy's father and has a vested interest in his son's well - being. Zeus might also be protective in some cases, despite their past differences, as Percy is a hero who often saves the world which benefits Zeus's realm as well.
Well, without reading the specific fanfiction, it's hard to say exactly who Percy is. But generally, in a 'champion of the gods' scenario, Percy would be a central figure. He might be a hero with unique powers, like being able to control certain elements or having superhuman strength. He could be a character who has to face various challenges and tasks on behalf of the gods, kind of like a chosen one in a fantasy story.
Another option could be Black Widow. She's very good at adapting to new situations and using her skills in different ways. For Percy, who is coming from a very different world, she could teach him how to be stealthy and use his powers in a more covert way. She could also help him with understanding the political side of the Avengers, like dealing with government agencies and such, which Percy may not be used to in his world of demigods.
Well, it could go either way. If the writer wants to create an interesting twist, Percy might be a villain in the Avengers fanfiction. But more often than not, given Percy's own heroic traits from his original story, he'd probably be a hero in the Avengers' universe, helping the Avengers fight against their common enemies.
The gods might show their protection in various ways. For example, they could directly intervene in battles Percy is in, using their divine powers to shield him from harm. They might also send him signs or omens to guide him away from danger.
Zeus is a possibility. As the king of the gods, he might see Percy's potential and adopt him to have an ally among the demigods. Another could be Poseidon, since Percy is already his son in the original story. It would be an interesting twist to have Poseidon formally adopt Percy in a more divine way.
Percy has his speed and agility. In the fanfiction, he might be able to use his demigod reflexes to dodge all of the Avengers' attacks. He could then quickly move in for a counter - attack. Also, his sword, Riptide, is a powerful weapon. It can cut through almost anything. He could use it to cut through the Avengers' weapons or their defenses if he gets close enough.
One idea could be a fanfiction where Percy uses his powers in a new and unique way to solve a problem that the gods themselves are struggling with. For example, he might find a way to stop a magical plague that is affecting both mortals and immortals. This would show his value and ingenuity, which the gods might appreciate.
Zeus is often one of the main gods showing possessiveness. He sees Percy as a powerful asset or a potential threat, so he wants to keep Percy in check. Poseidon, as Percy's father, also shows possessiveness in a different way. He wants to protect Percy but also use his powers for his own purposes sometimes.