I want to know given a connected (maybe we can assume it to be simply connected or linear) real semisimple lie group $G$ and one of its maximal parabolic group $P$, how can we embed the flag variety $G/P$ into some projective space?
If the lie algebra g is a split real form of its complexfication, then given any fundamental weight $\omega_i$ corresponding to the root $\alpha_i$, we can find the real irreducible highest weight module $V(\omega_i)$ such that $G$ can act on $\mathbb{P}(V(\omega_i))$, and the flag variety $G/P_{\alpha_i}$ can be identified with the orbit of the highest weight subspace $[\eta_{\omega_i}]$.
But if $g$ is not a split real form and what we know is a Cartan involution on it together with the restricted root space decomposition. I do not know how to construct a similar fundamental representation with respect to restricted roots.
There is one example one can deal with. Consider the lie group $\operatorname{SO}(p,q)$ where $p<q$ so its lie algebra is not a split real form. The cartan involution is sending $A\to A^{-T}$ on group level, so the maximal abelian is of rank $p$, and the restricted root system is of type $B_{p}$. The matrix group can act on $\mathbb{R}^{p,q}$. And indeed it acts transitively on isotropic lines in $\mathbb{R}^{p,q}$ and the stabilizer is the parabolic group corresponding to the first fundamental weight as usual. And after taking wedges of $k$ times ($k<p$), we can identify the flag varieties as isotropic $k$ grassmannians and embed it to the $kth$ wedge space which corresponds to the $kth$ fundamental representation.
But in general I do not know how to deal with it. And indeed what I concern is if we consider a real form of $E_6$ (or $E_7,E_8$) whose restricted root system is of type $F_4$, and pick $\alpha_1$ the first root in the restricted Dynkin diagram with $\omega_1$ the fundamental weight, can we find a representation $V(\omega_1)$ whose weight lattice can be described, and we can embed the first flag variety? Hope this clarifies.