  We prove six-term exact sequences of Pimsner-Voiculescu type for certain
subalgebras of the Cuntz-Pimsner algebras. This sequence may, in particular, be
applied to smooth subalgebras of the Quantum Heisenberg Manifolds in order to
compute the generators of their cyclic cohomology. Further, our results include
the known results for smooth crossed products. Our proof is based on a
combination of arguments from the setting of (Cuntz-)Pimsner algebras and the
Toeplitz proof of Bott-periodicity.
