  We report on the experimental observation of the quantum oscillations in
microwave magnetoabsorption of a high-mobility two-dimensional electron gas
induced by Landau quantization. Using original resonance-cavity technique, we
observe two kinds of oscillations in the magnetoabsorption originating from
inter-Landau-level and intra-Landau-level transitions. The experimental
observations are in full accordance with theoretical predictions. Presented
theory also explains why similar quantum oscillations are not observed in
transmission and reflection experiments on high-mobility structures despite of
very strong effect of microwaves on the dc resistance in the same samples.
