  Let X be an infinite compact metric space, \alpha : X \to X a minimal
homeomorphism, u the unitary implementing \alpha in the transformation group
C*-algebra, and S a class of separable nuclear C*-algebras that contains all
unital hereditary C*-subalgebras of C*-algebras in S. Motivated by the success
of tracial approximation by finite dimensional C*-algebras as an abstract
characterization of classifiable C*-algebras and the idea that classification
results for C*-algebras tensored with UHF algebras can be used to derive
classification results up to tensoring with the Jiang-Su algebra Z, we prove
that the transformation group C*-algebra tensored with a UHF algebra is
tracially approximately S if there exists a y in X such that a certain
C*-subalgebra is tracially approximately S. If the class S consists of finite
dimensional C*-algebras, this can be used to deduce classification up to
tensoring with Z for C*-algebras associated to minimal dynamical systems where
projections separate tracial states. This is done without making any
assumptions on the real rank or stable rank of either the transformation group
C*-algebra or the C*-subalgebra, nor on the dimension of X. The result is a key
step in the classification of C*-algebras associated to uniquely ergodic
minimal dynamical systems by their ordered K-groups. It also sets the stage to
provide further classification results for those C*-algebras of minimal
dynamical systems where projections do not necessarily separate traces.
