Let $G$ be a reductive group and let $P$ be a parabolic subgroup of $G$ all defined over $\mathbb{Z}$.
Also, let $F$ be a number field, is it true (and if so, please provide a reference) that
$$ \left(G/P\right)(F) = G(F)/P(F)$$
If it is not always true, is there a criterion for $G$, $P$ and $F$ so it will be true?



Rational Points of a Quotient of a Reductive Group by a Parabolic Subgroup
This is true: Borel/Tits,Groupes Reductifs, IHES, 27, 1965, Theorem 4.13(a).


