Stable equivalence of the weak closures of free groups convolution algebras

We prove in this paper that the von Neumann algebras associated to the free non-commutative groups are stably isomorphic, i.e. that they are isomorphic when tensorized by the algebra of all linear bounded operators on a separable, infinite dimensional Hilbert space. This gives positive evidence for an old question, due to R.V. Kadison (see also S. Sakai's book on W*-algebras), whether the von Neumann algebras associated to free groups are isomorphic or not.