Maximal amenable subalgebras arising from maximal amenable subgroups

We provide a general criterion to deduce maximal amenability of von Neumann subalgebras LΛ ⊂ LΓ arising from amenable subgroups Λ of discrete countable groups Γ. The criterion is expressed in terms of Λ-invariant measures on some compact Γ-space. The strategy of proof is different from S. Popa's approach to maximal amenability via central sequences [Po83], and relies on elementary computations in a crossed-product C *-algebra