In a large saucepan, heat the olive oil at medium heat.
Season the chicken breasts with salt, pepper and a dash of cayenne pepper. Place the chicken breasts in the hot pan and cook for 6-8 minutes on each side or until cooked thoroughly. Remove from the pan and set aside to cool for a couple of minutes. Slice into long strips.
For the spicy mayonnaise, mix the mayonnaise, salt, pepper, chili powder and cumin in a bowl.
Spread the spicy mayonnaise on one side of the tortillas. Place the arugula, apple, chicken and feta cheese on the tortilla, roll into a wrap and serve.