  Let G be a finite group acting linearly on the polynomial ring with invariant
ring R. If the action is small, then a classical result of Auslander gives in
dimension two a correspondence between linear representations of G and maximal
Cohen-Macaulay R-modules. We establish a correspondence for all linear actions
between representations and objects over the invariant ring by looking at
quotient module schemes (up to modification) instead of the modules of
covariants.
