On equivariant Hom-Leibniz cohomology

We study finite group actions on Hom-Leibniz algebras. We introduce equivariant cohomology of Hom-Leibniz algebras with coefficients in $$O_G$$ -Hom-algebras. We show that there is a cup-product operation in the graded equivariant Hom-Leibniz cohomology, which satisfies the graded Hom-Zinbiel relation.