  Let $X$ be a topological space and $G$ a compact connected Lie group acting
on $X$. Atiyah proved that the $G$-equivariant K-group of $X$ is a direct
summand of the $T$-equivariant K-group of $X$, where $T$ is a maximal torus of
$G$. We show that this direct summand is equal to the subgroup of $K_T^*(X)$
annihilated by certain divided difference operators. If $X$ consists of a
single point, this assertion amounts to the Weyl character formula. We also
give sufficient conditions on $X$ for $K_G^*(X)$ to be isomorphic to the
subgroup of Weyl invariants of $K_T^*(X)$.
