Generalized 2-Cocycles of Finite Groups and Maximal Orders

LetRbe a Dedekind domain with quotient fieldKand letGbe a finite group. Let α:G × G → R\{0} be a generalized 2-cocycle, i.e., not necessarily taking its values in the units ofR, and consider the generalized twisted group ringR * αG. In this paper we derive criteria forR * αGto be a graded maximalR-order, resp. a hereditaryR-order or a maximalR-order (inK * αG).