### Category of Noncommutative CW Complexes. II, by Do Ngoc Diep

We introduce in this paper the notion of noncommutative Serre
fibration (shortly, NCSF) and show that up to homotopy, every NCCW
complex morphism is some noncommutative Serre fibration. We then
deduce a six-term exact sequence for the periodic cyclic homology
and for K-theory of an arbitrary noncommutative Serre fibration.
We also show how to use this technique to compute K-theory and
cyclic theory of some noncommutative quotients.

Do Ngoc Diep <dndiep@math.ac.vn>