Adapter for a rolling assembly intended to be fitted to a passenger vehicle, with improved mountability and a high capacity for absorbing large deformations in the event of pinch shocks. The adapter has reinforcing element (15) of the axially outer end (9) wholly situated axially on the outside of bearing face (21) and radially on the outside of adapter seat (18), and a main reinforcement (17) having a radial superposition of at least two layers of reinforcers, the reinforcers being mutually parallel within one and the same layer and crossed with one another from one layer to the next. Each of the layers of main reinforcement (17) comprises reinforcers which make, with a circumferential direction (XX′) of the tire, an angle at least equal to 30°, and coated with a polymer material having an elastic modulus at 10% elongation at most equal to 70 MPa.