  Let $G$ be a reductive linear algebraic group. The simplest example of a
projective homogeneous $G$-variety in characteristic $p$, not isomorphic to a
flag variety, is the divisor $x_0 y_0^p+x_1 y_1^p+x_2 y_2^p=0$ in $P^2\times
P^2$, which is $SL_3$ modulo a non-reduced stabilizer containing the upper
triangular matrices. In this paper embeddings of projective homogeneous spaces
viewed as $G/H$, where $H$ is any subgroup scheme containing a Borel subgroup,
are studied. We prove that $G/H$ can be identified with the orbit of the
highest weight line in the projective space over the simple $G$-representation
$L(\lambda)$ of a certain highest weight $\lambda$. This leads to some strange
embeddings especially in characteristic $2$, where we give an example in the
$C_4$-case lying on the boundary of Hartshorne's conjecture on complete
intersections. Finally we prove that ample line bundles on $G/H$ are very
ample. This gives a counterexample to Kodaira type vanishing with a very ample
line bundle, answering an old question of Raynaud.
