Popa's W*-superrigidity conjecture for property (T) groups

Let $G$ be an ICC group with property (T), let $H$ be a group, and let $\operatorname{L}(G)$ and $\operatorname{L}(H)$ denote their group von Neumann algebras. An isomorphism $\operatorname{L}(G)\cong\operatorname{L}(H)$ is said to be induced by a character $G\to\mathbb T$ and a group isomorphism $G\to H$ up to conjugation by a unitary element when it has that form. Popa's conjecture. For any such $G$ and $H$, every isomorphism

$$\operatorname{L}(G)\cong\operatorname{L}(H)$$

is induced by a character $G\to\mathbb T$ and a group isomorphism $G\to H$, up to conjugation by a unitary element. This generalizes Connes' rigidity conjecture and incorporates Jones' formula for outer automorphisms. The statement is presented as a conjectural strengthening for property (T) groups; no resolution is given here.