LetRbe a discrete valuation ring andGa 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 a criterion forR*αG. to be separable over its center. This leads us to study the center and the prime ideals ofR*αG. Furthermore, we give some results on indecomposable modules overR*αG.