  We provide the ultimate explanation of one of the core features of
microwave-induced magnetoresistance oscillations in high mobility two
dimensional electron systems: the 1/4-cycle phase shift of minima. We start
with the radiation-driven electron orbits model with the novel concept of
scattering flight-time between Landau states. We calculate the extrema and
nodes positions obtaining an exact coincidence with the experimental ones. The
main finding is that the physical origin of the phase shift is a delay of
$\frac{\pi}{2}$ of the radiation-driven Landau guiding center with respect to
radiation, demonstrating the oscillating nature of the irradiated Landau
states.
  We analyze the dependence of this minima on radiation frequency and power and
its possible shift with the quality of the sample
