Let G be a reductive linear algebraic group. The simplest example of a
projective homogeneous G-variety in characteristic p, not isomorphic
to a Bag variety, is the divisor x(0)y(0)(p)+x(1)y(1)(p)+x(2)2)(p) = 0
in P-2 x P-2, which is SL(3) modulo a nonreduced stabilizer containin
g the upper triangular matrices. In this paper embeddings of projectiv
e homogeneous spaces viewed as G/H, where H is any sub-group scheme co
ntaining a Borel subgroup, are studied. We prove that G/H can be ident
ified with the orbit of the highest weight line in the projective spac
e over the simple G-representation L(lambda) of a certain highest weig
ht lambda. This leads to some strange embeddings especially in charact
eristic 2, where we give an example in the C-4-case lying on the bound
ary of Hartshorne's conjecture on complete intersections. Finally we p
rove that ample line bundles on G/H are very ample. This gives a count
erexample to Kodaira type vanishing with a very ample line bundle, ans
wering an old question of Raynaud.