Let $G$ be a compact connected Lie group and T be it's maximal torus. Let $\theta: G \rightarrow G$ be an involution on $G$ and let $G^\theta = \lbrace g \in G , \theta(g)=g \rbrace $.
I'm looking for an a simple the proof of the claim which says that $G/T$ has finitely many $G^\theta (\mathbb{C})$-orbits or just a sketch of the proof because I'm not very familiar with algebraic geometry and I would like to just know what are the ideas used to prove it.
Any help would be greatly appreciated! Thanks