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Let $G$ be a compact Lie group, $H$ a closed subgroup of maximal rank and $X$a topological $G$-space. We obtain a variety of results concerning thestructure of the $H$-equivariant K-ring $K_H^*(X)$ viewed as a module over the$G$-equivariant K-ring $K_G^*(X)$. One result is that the module has anonsingular bilinear pairing; another is that the module contains multipletswhich are analogous to the Gross-Kostant-Ramond-Sternberg multiplets ofrepresentation theory.

Character formul{\ae} and GKRS multiplets in equivariant K-theory