Rolling assembly comprising tire P, rim J, adapter connecting a bead and the rim. The adapter has axially outer (9) and inner (10) ends mounted on rim seat (7) having respective outer (16) and inner (20) reinforcers. Body (11) connects the outer (9) and inner (10) ends forming a single piece, an adapter seat (18) receives a bead and is situated at end (9), an adapter bearing face (21) in a plane perpendicular to the rotation axis, and situated on the axially inner face of outer end (9). Reinforcer (20) of end (9) is axially outside bearing face (21). The body comprises, opposite adapter seat (14), annular seat reinforcer (19) and the adapter comprises conductive strip (22) positioned over all or part of the circumferential perimeter of said adapter and along a complete path extending from adapter seat (14) to rim flange (8).