The invention concerns a method of manufacture of tires and a tire assembly drum having a body with a receiving surface for the products to be assembled, the body being mounted on a center shaft, and at least one lifting device situated at one of the ends of the receiving surface, the lifting device including a plurality of lifting fingers distributed circularly around the center shaft, the fingers extending appreciably radially and presenting a bearing surface for the products to be assembled, the fingers being controlled to be deployed essentially radially toward the outside of the drum.