  This is the first of three articles on the Fibered Isomorphism Conjecture of
Farrell and Jones for L-theory. We apply the general techniques developed in
[15] and [16] to the L-theory case of the conjecture and prove several results.
  Here we prove the conjecture, after inverting 2, for poly-free groups. In
particular, it follows for braid groups. We also prove the conjecture for some
classes of groups without inverting 2. In fact we consider a general class of
groups satisfying certain conditions which includes the above groups and some
other important classes of groups. We check that the properties we defined in
[15] are satisfied in several instances of the conjecture.
