Place turkey in a heavy-duty, zip-top plastic bag. Combine orange juice, garlic, pepper, and thyme; pour over turkey. Seal bag, and shake until turkey is well coated. Marinate in refrigerator 30 minutes, turning bag once.
Cut pepper in half lengthwise; remove and discard seeds and membrane. Flatten pepper with palm of hand. Coat grill rack with cooking spray; place on grill over medium-hot coals (350° to 400°). Place pepper, skin side down, on rack; grill, covered, 15 to 20 minutes or until charred. Place pepper in ice water until cool. Remove from water; peel and discard skin. Slice pepper into thin strips.
Combine pepper strips, cilantro, and next 4 ingredients in a small bowl, stirring well. Set aside.
Remove turkey from marinade; discard marinade. Place turkey on grill rack; grill, covered, 1 minute on each side or until turkey is tender. Transfer turkey to a serving plate. Spoon red pepper mixture evenly over turkey. Sprinkle with cheese.