  We report on the novel mechanism of electron scattering in hybrid Bose-Fermi
systems consisting of a two-dimensional electron gas in the vicinity of an
exciton condensate: We show that a pair-of-bogolons--mediated scattering proves
to be dominating over the conventional acoustic phonon channel and over the
single-bogolon scattering, even if the screening is taken into account. We
develop a microscopic theory of this effect, focusing on GaAs and MoS$_2$
materials, and find the principal temperature dependence of resistivity,
distinct from the conventional phonon--mediated processes. Further, we
scrutinize parameters and suggest a way to design composite samples with
predefined electron mobilities and propose a mechanism of electron pairing for
superconductivity.
