  We introduce the Farrell-Jones Conjecture with coefficients in an additive
category with G-action. This is a variant of the Farrell-Jones Conjecture about
the algebraic K- or L-Theory of a group ring RG. It allows to treat twisted
group rings and crossed product rings. The conjecture with coefficients is
stronger than the original conjecture but it has better inheritance properties.
Since known proofs using controlled algebra carry over to the set-up with
coefficients we obtain new results about the original Farrell-Jones Conjecture.
The conjecture with coefficients implies the fibered version of the
Farrell-Jones Conjecture.
