  Let $G$ be an almost simple simply-connected affine algebraic group over an
algebraically closed field $k$ of characteristic $p > 0$. If $G$ has type
$B_n$, $C_n$ or $F_4$, we assume that $p > 2$, and if $G$ has type $G_2$, we
assume that $p > 3$. Let $P \subset G$ be a parabolic subgroup. We prove that
the tangent bundle of $G/P$ is Frobenius stable with respect to the
anticanonical polarization on $G/P$.
