Isomorphism invariants for actions of sofic groups

For every countable group G, a family of isomorphism invariants for measurepreserving G-actions on probability spaces is defined. In the special case in which G is a countable sofic group, a special class of these invariants are computed exactly for Bernoulli systems over G. This leads to a complete classification of Bernoulli systems for many countable groups including all finitely generated linear groups. These results are combined with recent rigidity results of S. Popa to obtain classification results for Bernoulli shifts over special classes of groups G up to von Neumann equivalence and/or orbit equivalence.