Joint work (in progress) with P.W. Ng and V. Pestov.

Let A be a unital simple C*-algebra. If the unitary group of A with the norm topology is amenable, then A is stably finite and using a result of Paterson, is nuclear.

Using Elliott Classification Program and a deep result of M.-P. and P. Malliavin, we show that the converse is true for a (large) class of stably finite nuclear unital simple C*-algebras.