  We introduce a new spectral sequence called the p-chain spectral sequence
which converges to the (co-)homology of a contravariant C-space with
coefficients in a covariant C-spectrum for a small category C. It is different
from the corresponding Atiyah-Hirzebruch type spectral sequence. It can be used
in combination with the Isomorphism Conjectures of Baum-Connes and
Farrell-Jones to compute algebraic K- and L-groups of group rings and
topological K-groups of reduced group C*-algebras.
