  We investigate the cosmological behavior of mimetic F(R) gravity. This
scenario is the F(R) extension of usual mimetic gravity classes, which are
based on re-parametrizations of the metric using new, but not propagating,
degrees of freedom, that can lead to a wider family of solutions. Performing a
detailed dynamical analysis for exponential, power-law, and arbitrary F(R)
forms, we extracted the corresponding critical points. Interestingly enough, we
found that although the new features of mimetic F(R) gravity can affect the
universe evolution at early and intermediate times, at late times they will not
have any effect, and the universe will result at stable states that coincide
with those of usual F(R) gravity. However, this feature holds for the late-time
background evolution only. On the contrary, the behavior of the perturbations
is expected to be different since the new term contributes to the perturbations
even if it does not contribute at the background level.
