Quantum-mechanical transport cross sections are accurately computed from recent spectroscopic potentials for the three lowest energy levels of the molecular ion HeAr+. Statistical and ground state combinations of the cross sections are used to compute the transport coefficients describing the motion of Ar+ ions through He gas at 4.35 K. The calculated mobilities do not show the rapid decrease of the experimental values as the ratio of the electric field strength to the gas number, density becomes very small. The experimental observations therefore are not due to the effects of orbiting resonance.