  In this paper we prove that the cohomology groups with compact support of
stacks of shtukas are modules of finite type over a Hecke algebra. As an
application, we extend the construction of excursion operators, defined by V.
Lafforgue on the space of cuspidal automorphic forms, to the space of
automorphic forms with compact support. This gives the Langlands
parametrization for some quotient spaces of the latter, which is compatible
with the constant term morphism.
