Maximal amenable von Neumann subalgebras arising from maximal amenable subgroups

We provide a general criterion to deduce maximal amenability of von Neumann subalgebras $L\mathrm{\Lambda }\subset L\mathrm{\Gamma }$ arising from amenable subgroups $\mathrm{\Lambda }$ of discrete countable groups $\mathrm{\Gamma }$. The criterion is expressed in terms of $\mathrm{\Lambda }$-invariant measures on some compact $\mathrm{\Gamma }$-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.