  We prove a conjecture of Broue about the Jordan decomposition of blocks of
finite reductive groups. We show that a block of a finite connected reductive
group, in non-describing characteristic, is Morita-equivalent to a
quasi-isolated block of a Levi subgroup. This involves showing that some local
system over a Deligne-Lusztig variety has its mod l cohomology concentrated in
one degree. We reduce this question to a question about tamely ramified local
systems by proving that the category of perfect complexes for the group is
generated by the images of the Deligne-Lusztig functors. Then, we describe the
ramification at infinity of local systems associated to characters of tori.
