Generalized twisted group rings

Let R be a domain and G a group. Let α:G×G→R∖{0} be a generalized 2-cocycle, i.e., not necessarily taking its values in the units of R, and consider the generalized twisted group ring R*αG. First we investigate the graded structure of R*αG, in particular we give conditions under which R*αG is gr-hereditary, respectively a gr-maximal order. Next, we derive criteria for R*αG to be a tame order, respectively a maximal order over some central subring. We also derive conditions under which R*αG is an Azumaya algebra.