Orbits of Real Semisimple Lie Groups on Real Loci of Complex Symmetric Spaces

Let G be a complex semisimple algebraic group and X be a complex symmetric homogeneous G-variety. Assume that both G, X as well as the G-action on X are defined over real numbers. Then G(.) acts on X(.) with finitely many orbits. We describe these orbits in combinatorial terms using Galois cohomology, thus providing a patch to a result of Borel and Ji.