Equivariant formality of isotropy actions on homogeneous spaces defined   by Lie group automorphisms
  We show that the isotropy action of a homogeneous space $G/K$, where $G$ and $K$ are compact, connected Lie groups and $K$ is defined by an automorphism on $G$, is equivariantly formal and that $(G, K)$ is a Cartan pair. 
Oliver Goertsches, Sam H. Noshari
math.DG math.AT