When the large Doppler shifts of hot-electron-ring ECRH absorption are taken into account, the spatial location of the bulk of the energy absorption can be significantly shifted from the cold-plasma resonance region. The high parallel velocity electrons absorb most of the wave energy, thereby shielding the bulk of the electron distribution from the heating source. A simple one-dimensional model of this process has been formulated, based on a right-hand circularly polarized wave which is incident from the high-field side in the parallel direction. In this model, less than 1% of the electrons absorb more than 90% of the wave energy for the case of 30-keV maximum parallel electron energy, 28-GHz microwaves, and a 1-m magnetic field scale length. The effect should be included in power balance models and Fokker-Planck velocity distribution calculations. The Doppler shift also appears for a variety of ray-tracing code calculations in the MFTF-B thermal barrier region.