Results from a numerical study of the nonlinear interaction between large-amplitude Alfv¿n waves and the low-altitude auroral magnetosphere and ionosphere are presented. In the model the Alfv¿n wave encounters collisionless resistive dissipation when and where the effective parallel drift of electrons carrying the wave field-aligned current density exceeds a critical threshold corresponding to onset of current-driven microinstability. The resulting parallel electric field and parallel potential drop introduce frequency, amplitude, and perpendicular length-scale dependence in the absorption of Alfv¿n wave power. Analysis of the power flow shows that (1) most of the power generated by a constant-current source in the magnetosphere and carried by relatively small-amplitude, high-frequency, and short transverse wavelength Alfv¿n waves is reflected at low altitudes by the wave-induced collisionless resistive layer (RL); (2) Alfv¿n wave power is absorbed primarily in the RL except when stimulated by a constant-voltage generator, wherein ionospheric Joule heating dominates the absorption at large transverse length scales; (3) the absorption is high (≈0.8) at length scales of 10--20 km (ionospheric projection) for constant voltage source conditions; and (4) the relation between the wave-induced parallel potential drop and wave field-aligned current is linear with proportionality constant of order 109 Ω-m2 over much of the range of interest. Correspondence between predicted properties and satellite observations is demonstrated.