Preheat grill to high heat (450° to 500°). Slice tops off of peppers, reserving tops; scoop out and discard seeds. Toss peppers with oil, salt, and pepper. Grill peppers and tops on all sides 2 to 3 minutes or until pepper bottoms are well-marked and softened, but still hold their shape.
Combine crab and next 6 ingredients in a large bowl; stir gently. Divide crab mixture evenly among peppers. Grill stuffed peppers, covered with grill lid, 5 minutes. Arrange on a platter, and serve with lemon wedges.