Moduli of equivariant sheaves and Kronecker-McKay modules

We extend Álvarez-Cónsul and King description of moduli of sheaves over projective schemes to moduli of equivariant sheaves over projective Γ-schemes, for a finite group Γ. We introduce the notion of Kronecker-McKay modules and construct the moduli of equivariant sheaves using a natural functor from the category of equivariant sheaves to the category of Kronecker-McKay modules. Following Álvarez-Cónsul and King, we also study theta functions and homogeneous co-ordinates of moduli of equivariant sheaves.