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 ⊂ 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.