Graded components of local cohomology modules of invariant rings

Let A be a regular domain containing a field K of characteristic zero, G be a finite subgroup of the group of automorphisms of A and be the ring of invariants of G. Let and be standard graded with and for all i. Extend the action of G on A to S by fixing X-i. Note . Let I be an arbitrary homogeneous ideal in R. The main goal of this paper is to establish a comparative study of graded components of local cohomology modules that would be analogs to those proven in the paper [5] for where J is an arbitrary homogeneous ideal in S.