Orbit equivalence for Cantor minimal Z^d-systems
  We show that every minimal action of any finitely generated abelian group on the Cantor set is (topologically) orbit equivalent to an AF relation. As a consequence, this extends the classification up to orbit equivalence of minimal dynamical systems on the Cantor set to include AF relations and Z^d-actions. 
Thierry Giordano, Hiroki Matui, Ian F. Putnam, Christian F. Skau