Preheat oved to 400. Cut 8 12-inch squares heavy-duty aluminum foil. Brush each sheet lightly with oil. In a large mixing bowl, toss potatoes with remaining oil. Add onion, pepper and half the cheese. Divide mixture between foil sheets and top with remaining cheese. Fold foil packets into "purses," taking care to leave space in the top so cheese won't stick.
Bake until potatoes can be pierced with a fork, about 50 minutes. Alternatively, cook on the grill until fork tender, about 50 minutes.