Recent observations have indicated that in addition to the quasi-static acceleration of electrons in inverted V structures, auroral electrons frequently have a spectrum that is broad in energy and confined to parallel pitch angles, indicative of acceleration in low-frequency waves. Test particle models have indicated that these electrons may be accelerated by the parallel electric fields in kinetic Alfv¿n waves. However, such models are not self-consistent, in that the wave structure is not influenced by the accelerated particles. A nonlocal kinetic theory of electrons along auroral field lines is necessary to provide this self-consistency. Results from such a model based on electron motions on dipole field lines are presented. For a typical Alfv¿n speed profile, kinetic effects lead to significant energy dissipation when the electron temperature exceeds ~100 eV. The dissipation generally occurs near the peak of the Alfv¿n speed profile. This dissipation generally increases with increasing temperature and decreasing perpendicular wavelength up to ~1 keV and 10 km, respectively. At larger temperatures and smaller perpendicular wavelengths the dissipation begins to decrease and the ionospheric Joule dissipation goes to zero, indicating that the wave is reflected from the dissipation region. Dissipation in the 0.1--1.0 Hz band is structured by the modes of the ionospheric Alfv¿n resonator.