  Using the simple but robust model of a shell of dark matter (DM) around a
Schwarzschild black hole (BH), represented by the mass ratio of the shell and
BH ${\Delta}M/M$, the shell extension ${\Delta}r_s$ and its inner radius $r_s$,
we study the influence of DM on the spacetime structure and geodesic motion,
and provide a classification of the BH+DM shell spacetimes according to the
properties of the stable circular geodesics governing Keplerian disks. We focus
our attention on the epicyclic motion around circular geodesics that can be
related to observational phenomena in X-ray radiation from Keplerian accretion
disks, assumed to be influenced by the DM shell only gravitationally. We give
the frequencies of the orbital and epicyclic motions and discuss their
properties in terms of the parameters governing the DM shell. Using the
frequencies in relevant variants of the standard geodesic model of
high-frequency quasiperiodic oscillations (HF QPOs), we test the role of DM by
fitting the HF QPO data from some microquasars and active galactic nuclei with
supermassive BHs where no variant of the geodesic model applied in the standard
vacuum BH background is able to explain the data. We thus provide a robust
review of the applicability of the geodesic model of HF QPOs, and also provide
limits on the amount of DM around a BH. We demonstrate that the geodesic model
could be well applied to most observations of active galactic nuclei, with
strong restrictions on the amount of invisible matter around BHs.
