Bivariant K-theory of generalized Weyl algebras

We compute the isomorphism class in KKalg of all noncommutative generalized Weyl algebras A D C[h].σ; P /, where σ.h/ D qh C h0 is an automorphism of C[h], except when q ¤ 1 is a root of unity. In particular, we compute the isomorphism class in KKalg of the quantum Weyl algebra, the primitive factors Bλ of U.sl2/ and the quantum weighted projective lines O.W Pq.k; l//.