Let G be a connected complex reductive algebraic group. Denote by W the Weyl group and by X the flag variety of G. Suppose Q is a closed real Lie subgroup of G having finitely many orbits on X and let T Q ∗X be the conormal variety of Q-action. The Grothendieck group κ Q ( x) of constructible sheaves on X whose characteristic variety is contained in T Q ∗X has a natural W-module structure, given by the action of intertwining operators. On the other hand, we consider the W-module structure on the top-dimensional Borel-Moore homology group H 2n(T Q ∗X, C) (with complex coefficients) defined by Lusztig. We show that the characteristic cycle map ϰ Q(X) c → H 2n(T Q ∗X, C) is a homomorphism of W-modules.