  Let G denote a compact connected Lie group with torsion-free fundamental
group acting on a compact space X such that all the isotropy subgroups are
connected subgroups of maximal rank. Let $T\subset G$ be a maximal torus with
Weyl group W. If the fixed-point set $X^T$ has the homotopy type of a finite
W-CW complex, we prove that the rationalized complex equivariant K-theory of X
is a free module over the representation ring of G. Given additional conditions
on the W-action on the fixed-point set $X^T$ we show that the equivariant
K-theory of X is free over R(G). We use this to provide computations for a
number of examples, including the ordered n-tuples of commuting elements in G
with the conjugation action.
