Generalized Cuntz-Krieger algebras

To a special embedding Φ Φ of circle algebras having the same spectrum, we associate an r-discrete, locally compact groupoid, similar to the Cuntz-Krieger groupoid. Its C ∗ C^* -algebra, denoted O Φ OΦ , is a continuous version of the Cuntz-Krieger algebras O A O_A . The algebra O Φ OΦ is generated by an A T -algebra and a nonunitary isometry. We compute its K-theory under the assumption that the A T -algebra is simple.