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(Tk ) ×θ Z are in fact inductive limits of circle algebras. Introduction In recent years there has been rapid progress in classification of nuclear simple C .
