We report on 1/B-periodic magnetoresistance oscillations in a two-dimensional electron system induced by microwave irradiation. They are only present in high mobility samples when an initial light pulse has created a persistent photoconductive channel in the adjacent donor layer. The oscillations manifest a geometric commensurability between the electron cyclotron orbit and a steady-state periodic density modulation. The latter may originate from the non-linear dynamical screening of a surface acoustic wave potential in the persistent photoconductive channel, triggered by the incident monochromatic microwave.