1. In a small bowl, combine mayonnaise, chilies, adobo sauce and lime juice. Season with pepper. Keep chilled until ready to serve. Makes about 1/2 cup. (The mixture may be made up to three days in advance.)
2. Form pockets in halved pitas. Divide mayonnaise mixture in half and spread a spoonful deep inside each pocket. Divide turkey, cheese and avocado slices among pockets, tucking them inside. Divide sprouts among the pockets. Spread remaining mayonnaise on top. Wrap in foil and refrigerate.