Wreath-like products of groups and their von Neumann algebras II: Outer automorphisms

Given a countable group G, let L(G) denote its von Neumann algebra. For a wide class of infinite conjugacy classes (ICC) groups with Kazhdan’s property (T), we confirm V. F. R. Jones’ conjecture asserting that Out(L(G))≅Char(G)⋊Out(G). As an application, we show that, for every countable group Q, there exists an ICC group G with property (T) such that Out(L(G))≅Q.