  Recent observations of gamma-rays with the Fermi Large Area Telescope (LAT)
in the direction of the inner Galaxy revealed a mysterious GeV excess. Its
intensity is significantly above predictions of the standard model of cosmic
rays (CRs) generation and propagation with a peak in the spectrum around a few
GeV. Popular interpretations of this excess are due to either spherically
distributed annihilating dark matter (DM) or abnormal population of millisecond
pulsars. We suggested an alternative explanation of the excess through the CR
interactions with molecular clouds in the Galactic Center (GC) region. We
assumed that the excess could be imitated by the emission of molecular clouds
with depleted density of CRs with energies below ~ 10 GeV inside. A novelty of
our work is in detailed elaboration of the depletion mechanism of CRs with the
mentioned energies through the "barrier" near the cloud edge formed by the
self-excited MHD turbulence. Such depletion of CRs inside the clouds may be a
reason of deficit of gamma rays from the Central Molecular Zone (CMZ) at
energies below few GeV. This in turn changes the ratio between various emission
components at those energies, and may potentially absorb the GeV excess by
simple renormalization of key components.
