An infinite family of non-isomorphic C*-algebras with identical K-theory
  We exhibit a countably infinite family of simple, separable, nuclear, and mutually non-isomorphic C*-algebras which agree on K-theory and traces. The algebras do not absorb the Jiang-Su algebra Z tensorially, answering a question of N. C. Phillips. They are also pairwise shape and Morita equivalent. The distinguishing invariant is the radius of comparison, a non-stable invariant of the Cuntz semigroup. 
Andrew S. Toms