  Projectively coresolved Gorenstein flat modules were introduced by Saroch and
Stovicek and were shown to be Gorenstein projective. We give characterizations
of Gorenstein projective, Gorenstein flat and projectively coresolved
Gorenstein flat modules over a group ring $RG$, where $G$ is an
$\textrm{LH}\mathfrak{F}$-group or a group of type $\Phi_R$ and $R$ is a
commutative ring of finite Gorenstein weak global dimension. In this situation,
we prove that every Gorenstein projective $RG$-module is projectively
coresolved Gorenstein flat. We deduce that every Gorenstein projective
$RG$-module is Gorenstein flat. The existence of weak characteristic modules
for a group $G$ over a commutative ring $R$ plays a central role in our
results. Furthermore, we determine the Gorenstein homological dimension of an
$\textrm{LH}\mathfrak{F}$-group over a commutative ring of finite Gorenstein
weak global dimension.
