Crossed group rings of finite groups and rings of $p$-adic integers with finitely many indecomposable integral representations

Let $F$ be a finite extension of the field $Q_p$ of rational $p$-adic numbers, $R$ the ring of all integral elements of $F$, $ R^*$ the multiplicative group of $R$, $G$ a finite group, and $\Lambda=(G,R,\lambda)$ the crossed group ring of $G$ and $R$ with the factor system $\{\lambda_{a,b}\}$ ($\lambda_{a,b}\in R^*$; $a,b\in G$). A classification is given of the rings $\Lambda$ for which the number of indecomposable $R$-representations is finite. When $\Lambda$ is a group ring, this problem was solved in papers by Faddeev, Borevich, Gudivok, Yakobinskii, and others.
Bibliography: 22 titles.