On invariant von Neumann subalgebras rigidity property

We say that a countable discrete group Γ satisfies the invariant von Neumann subalgebras rigidity (ISR) property if every Γ- subalgebra M in L(Γ) is of form L(Λ) for some normal subgroup Λ◁Γ. show many “negatively curved” groups, including all torsion free non-amenable hyperbolic groups and with positive first L2-Betti number under mild assumption, certain finite direct product them have this property. also discuss whether torsion-free assumption can be relaxed.