  We prove, for all reductive groups, that the cohomology sheaves with compact
support of stacks of shtukas are ind-smooth over $(X - N)^I$ and that their
geometric generic fibers are equiped with an action of $\text{Weil}(X - N,
\overline{\eta})^I$. Our method does not use any compactification of stacks of
shtukas.
