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We provide the ultimate explanation of one of the core features ofmicrowave-induced magnetoresistance oscillations in high mobility twodimensional electron systems: the 1/4-cycle phase shift of minima. We startwith the radiation-driven electron orbits model with the novel concept ofscattering flight-time between Landau states. We calculate the extrema andnodes positions obtaining an exact coincidence with the experimental ones. Themain 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 toradiation, demonstrating the oscillating nature of the irradiated Landaustates.  We analyze the dependence of this minima on radiation frequency and power andits possible shift with the quality of the sample

Evidence of radiation-driven Landau states in 2D electron systems: magnetoresistance oscillations phase shift