Some classifiable groupoid C∗-algebras with prescribed K-theory

Given a simple, acyclic dimension group G 0 and countable, torsion-free, abelian group G 1 , we construct a minimal, amenable, étale equivalence relation, R , on a Cantor set whose associated groupoid C ∗ -algebra, C ∗ ( R ) , is tracially AF, and hence classifiable in the Elliott classification scheme for simple, amenable, separable C ∗ -algebras, and with K ∗ ( C ∗ ( R ) ) ≅ ( G 0 , G 1 ) .