  We report on experimental and theoretical studies of microwave-induced
resistance oscillations in a two-dimensional electron gas over a wide range of
microwave intensities. We observe a distinct crossover from linear to sublinear
power dependence of the oscillation amplitude and a concomitant narrowing of
the oscillation extrema. To explain our observations we propose a theory based
on the quantum kinetic equation at arbitrary microwave power. Taken together,
these findings demonstrate a crucial role of multiphoton processes at elevated
microwave intensities.
