Let k be a commutative ring, A and ℬ – two k-linear categories with an action of a group G. We introduce the notion of a standard G-equivalence from Kpbℬ to KpbA, where KpbA is the homotopy category of finitely generated projective A-complexes. We construct a map from the set of standard G-equivalences to the set of standard equivalences from Kpbℬ to KpbA and a map from the set of standard G-equivalences from Kpbℬ to KpbA to the set of standard equivalences from Kpb(ℬ/G) to Kpb(A/G), where A/ G denotes the orbit category. We investigate the properties of these maps and apply our results to the case where A= ℬ= R is a Frobenius k-algebra and G is the cyclic group generated by its Nakayama automorphism ν. We apply this technique to obtain the generating set of the derived Picard group of a Frobenius Nakayama algebra over an algebraically closed field.