$W^{\ast }$ and $C^{\ast }$-superrigidity results for coinduced groups

In this paper we explore a generic notion of superrigidity for von Neumann algebras $L(G)$ and reduced $C^{\ast }$-algebras $C_r^{\ast }(G)$ associated with countable discrete groups $G$. This allows us to classify these algebras for various new classes of groups $G$ from the realm of coinduced groups.