Mod p equivariant cohomology of homogeneous spaces

Let (G,K) be a compact Lie pair. Then K acts on the homogeneous space G/K b y left translation. In [3], Shiga has studied the condition on the pair (G, K) that the fibration G/K --> EK x(K) G/K --> BK is totally non-cohomologou s to zero with respect to the real field from the viewpoint of the equivari ant de Rham cohomology and its model. We generalize the main theorem in [3] on the ordinary cohomology theory with coefficients in any field. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 55N91; 55T15.