LAUSR

We consider twisted equivariant K-theory for actions of a compact Lie group G on a space X where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational spectral sequence a la Segal has a simple E2-term expressible as invariants under the Weyl group of G. Specifically, if T is a maximal torus of G, they are invariants of the π1(XT)-equivariant Bredon cohomology of the universal cover of XT with suitable coefficients. In the case of the inertia stack ΛY, this term can be expressed using the cohomology of YT and algebraic invariants associated with the Lie group and the twisting. A number of calculations are provided. In particular, we recover the rational Verlinde algebra when Y = {*}.We consider twisted equivariant K-theory for actions of a compact Lie group G on a space X where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational spectral sequence a la Segal has a simple E2-term expressible as invariants under the Weyl group of G. Specifically, if T is a maximal torus of G, they are invariants of the π1(XT)-equivariant Bredon cohomology of the universal cover of XT with suitable coefficients. In the case of the inertia stack ΛY, this term can be expressed using the cohomology of YT and algebraic invariants associated with the Lie group and the twisting. A number of calculations are provided. In particular, we recover the rational Verlinde algebra when Y = {*}.