The body unit for an airbag can be brought to a required inflated shape. A sector (54) for setting the inflated shape is made in the form of strips. At both end positions, it has a fixing side layer (34) running transversely to the vehicle. A circumferential region (38) of the fixing side layer is sewn to the circumferential end region (36) of a layer (32) facing the passenger. When the airbag body (10) inflates, the region of the passenger side layer sewn to the shape setting sector limits the inflated airbag to the desired shape.
