Structure of II1 factors arising from free Bogoljubov actions of arbitrary groups

In this paper, we investigate several structural properties for crossed product II1 factors M arising from free Bogoljubov actions associated with orthogonal representations π:G→O(HR) of arbitrary countable discrete groups. Under fairly general assumptions on the orthogonal representation π:G→O(HR), we show that M does not have property Gamma of Murray and von Neumann. Then we show that any regular amenable subalgebra A⊂M can be embedded into L(G) inside M. Finally, when G is assumed to be amenable, we locate precisely any possible amenable or Gamma extension of L(G) inside M.