  We prove Gieseker conjecture for an homogeneous space $X$, saying that if $X$
has no non-trivial tame coverings then it has no non-trivial regular singular
$\mathscr{O}_X$-coherent $\mathscr{D}_{X/k}$-modules. In order to do so we
prove a K\"unneth formula for the regular singular stratified fundamental group
and a base change for Gauss-Manin stratifications in the non-proper case.
