Mix gingerroot, lime juice, soy sauce, sesame oil, red pepper and garlic in glass or plastic dish. Stir in shrimp until well coated. Cover and refrigerate 15 minutes.
Heat coals or gas grill. Remove shrimp from marinade; reserve marinade. Thread bell peppers, mushrooms, shrimp and onions alternately on each of twelve 6-inch skewers. Brush lightly with marinade.
Cover and grill kabobs about 4 inches from medium heat about 6 minutes, brushing with marinade and turning once, until shrimp are pink and firm and vegetables are crisp-tender. Discard marinade.