Action of finite groups on Rees algebras and Gorensteinness in invariant subrings

Let G be a finite group of order N and assume that G acts on a Cohen-Macaul ay local ring A as automorphisms of rings. Let N be a unit in A. For a give n G-stable ideal I in A we denote by R(I)= +I-n greater than or equal to 0( n) and G(I)= +I-n greater than or equal to 0(n)/In+1 the Rees algebra and t he associated graded ring of I, respectively. Then G naturally acts on R(I) and G(1) too. In this paper the conditions under which the invariant subri ngs R(I)G of R(I) are Cohen-Macaulay and/or Gorenstein rings are described in connection with the corresponding ring-theoretic properties of G(I)(G) a nd the a-invariants a(G(I)(G)) of G(I)(G). Consequences and some applicatio ns are discussed.