  Let $\kk$ be a commutative ring, $\AAA$ and $\BB$ -- two $\kk$-linear
categories with an action of a group $G$. We introduce the notion of a standard
$G$-equivalence from $\Kb\BB$ to $\Kb\AAA$. We construct a map from the set of
standard $G$-equivalences to the set of standard equivalences from $\Kb\BB$ to
$\Kb\AAA$ and a map from the set of standard $G$-equivalences from $\Kb\BB$ to
$\Kb\AAA$ to the set of standard equivalences from $\Kb(\BB/G)$ to
$\Kb(\AAA/G)$. We investigate the properties of these maps and apply our
results to the case where $\AAA=\BB=R$ is a Frobenius $\kk$-algebra and $G$ is
the cyclic group generated by its Nakayama automorphism $\nu$. We apply this
technique to obtain the generating set of the derived Picard group of a
Frobenius Nakayama algebra over an algebraically closed field.
