  Let $\cP=G/P$ be a homogeneous projective variety with $G$ a reductive group
and $P$ a parabolic subgroup. In positive characteristic we exhibit for $G$ of
low rank a Karoubian complete strongly exceptional poset of locally free
sheaves appearing in the Frobenius direct image of the structure sheaf of
$G/P$. These sheaves are all defined over $\bbZ$, so by base change provide a
Karoubian complete strongly exceptional poset on $\cP$ over $\bbC$, adding to
the list of classical results by Beilinson and Kapranov on the Grassmannians
and the quadrics over $\bbC$.
