Graded equivalence theory with applications (Q1891496)

The first goal of this paper is to show that if two \(G\)-graded rings \(R\) and \(S\) have the property that their categories of graded modules are equivalent via a functor commuting with suspensions, then for any subgroup \(H\) of \(G\) there exist equivalences between the categories of modules graded by the \(G\)-set of right \(H\)-cosets over \(R\) and \(S\), respectively. This result is then used to pass results holding for rings graded by subgroups \(H\) to rings graded by the group \(G\).