On the equivariant cohomology of ${\mathbb{Z}}_2\times {\mathbb{Z}}_k$-symmetric spaces

$\mathrm{\Gamma }$-symmetric spaces are a vast generalization of symmetric spaces. Previous results make it conceivable that their isotropy action is equivariantly formal, and we provide evidence for this in case that $\mathrm{\Gamma }={\mathbb{Z}}_2\times {\mathbb{Z}}_k$. This in particular implies that ${\mathbb{Z}}_2\times {\mathbb{Z}}_k$-symmetric spaces are formal in the sense of Rational Homotopy Theory.