. Developing new technical aspects in Popa's deformation/rigidity theory we introduce several new classes of W * -superrigid groups which appear as direct products, semidirect products with non-amenable core and iterations of amalgamated free products and HNN-extensions. As a byproduct we obtain new rigidity results in C * -algebra theory including additional examples of C * -superrigid groups and explicit computations of symmetries of reduced group C * -algebras.

In this paper we explore a generic notion of superrigidity for von Neumann algebras L(G) and reduced C * -algebras C * r (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. I.C. has been supported in part by the NSF grants DMS-1600688, FRG DMS-1854194 and a CDA award from the University of Iowa. A.D-A. was supported in part by the AGEP-supplemental grant. D.D. holds the postdoctoral fellowship fundamental research 12T5221N of the Research Foundation -Flanders.