The low-temperature photoluminescence ͑PL͒ of GaAs/ AlGaAs quantum wells and heterojunctions containing a high mobility two-dimensional electron gas ͑2DEG͒ is studied under microwave ͑mw͒ irradiation of 36 GHz. The analysis of the mw-modulated PL ͑MPL͒ spectra allows us to elucidate the effects of mw radiation on the 2DEG. For low magnetic field strengths ͑B Ͻ 0.5 T͒, we show that the MPL spectral shape is due to energy redistribution of the photoexcited holes, as affected by the mw-heated 2DEG. For the mechanism that causes the nonequilibrium hole-energy redistribution, we propose that it is the interaction of the holes with low-energy acoustic phonons emitted by the mw-heated 2DEG. This underlying physical mechanism gives rise to the optically detected 2DEG cyclotron resonance at low B. For B Ͼ 0.5 T, optically detected resonances are observed at B values that depend on the 2DEG density, and they occur near integer electron filling factors. We argue that these resonances result from a slight 2DEG density increase under mw irradiation with a concurrent, low-energy PL spectral shift due to small band-gap narrowing.