Classification of type III Bernoulli crossed products

Crossed products with noncommutative Bernoulli actions were introduced by Connes as the first examples of full factors of type III. This article provides a complete classification of the factors (P,ϕ)Fn⋊Fn(P,ϕ)Fn⋊Fn, where FnFn is the free group and P is an amenable factor with an almost periodic state ϕ. We show that these factors are completely classified by the rank n   of the free group FnFn and Connes's Sd-invariant. We prove similar results for free product groups, as well as for classes of generalized Bernoulli actions.