Peel then cut chayote in half. Remove and discard seeds. Cut into 1/4-inch thick sticks (3 to 4 inches long).
Using sharp knife, cut and peel white pith from oranges. Working over bowl containing chayote, cut segments free from membranes, allowing segments to fall into bowl. Squeeze orange juice from membrane.
Add lime juice, cilantro, salt and red pepper. Toss; cover with plastic wrap. Let stand about 30 minutes or until chayote can be bent slightly.
Place tortillas on microwavable plate. Cover with waxed paper, and microwave 45 to 60 seconds or until warm.
Fill each tortilla with a few slices of turkey, chayote salad and cheese.