Graded Components of Local Cohomology Modules Over Invariant Rings-II

Let A be a regular ring containing a field K of characteristic zero and let R=A[X-1,...,X-m].Consider Ras standard graded with deg A=0 and deg Xi=1foralli.LetGbeafinitesubgroup of GL(m)(A).Let Gact linearly on R fixing A.Let S = R-G. In this paper, we presenta comprehensive study of graded components of local cohomology module HiI(S),where Iis anarbitrary homogeneous ideal in S. We prove stronger results when G subset of GL(m)(K).Some of our results are new even in the case when A is a field.