Heat gas or charcoal grill. In medium bowl, mix ground beef, chili powder and ground red pepper. Shape mixture into 4 (4-inch) patties, 1/2 inch thick. Spray both sides of onion slices with cooking spray or brush with oil.
When grill is heated, place patties and onion slices on gas grill over medium heat or on charcoal grill over medium coals; cover grill. Cook 11 to 13 minutes, turning patties and onion slices once, until thermometer inserted in center of patties reads 160°F. During last 2 minutes of cooking, place buns, cut sides down, on grill and cheese on patties; cook 1 to 2 minutes or until buns are golden brown and cheese is melted.
Place patties on bottom halves of buns. Top with onion slices. Cover with top halves of buns.