Classification of simple C * - algebras and higher dimensional noncommutative tori

We show that unital simple C-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C-algebras can be classified by their ordered K-theory. We apply this classification result to show that certain simple crossed products are isomorphic if they have the same ordered K-theory. In particular, irrational higher dimensional noncommutative tori of the form C(T)×θ Z are in fact inductive limits of circle algebras.