In a small bowl, cover the turkey breast strips with barbecue sauce. Cover the bowl with cling film and allow to marinade for a few hours or overnight.
When you're ready to cook the filling, set a tablespoon of the raw onion aside for salad filling. In a frying pan, fry the rest of the sliced onion in olive oil.
When the onion is softened, add the turkey in barbecue sauce and cook through on a medium heat. Allow to cool slightly.
Lay the wraps out flat on four plates. Line a quarter of each wrap's surface area with 3 leaves of gem lettuce and spoon some warm turkey in sauce on top of the lettuce.
Scatter over the remaining raw onion and diced red pepper. Roll up the wraps into a cone, serve immediately.