  We present the first measurements of inter-subband absorption of microwaves
in surface electrons on liquid helium subjected to perpendicular magnetic field
B. In quantizing B, the power absorption shows intermittent regions of enhanced
and suppressed absorption. This behavior is caused by strong variation of the
excited-electron decay rate with B. Particularly, fast decay due to elastic
scattering provides condition for strong absorption and overheating of the
electron system, while slow decay due to inelastic scattering limits absorption
and causes its saturation. An unexpected feature is the strong suppression of
absorption at magnetic fields where the inter-subband energy splitting is a
multiple number of the cyclotron energy.
