Rational equivariant cohomology theories with toral support

For an arbitrary compact Lie group\n[math] , we describe a model\nfor rational\n[math] –spectra\nwith toral geometric isotropy and show that there is a convergent Adams spectral\nsequence based on it. The contribution from geometric isotropy at a subgroup\n[math] of the maximal\ntorus of\n[math] is captured\nby a module over\n[math]\nwith an action of\n[math] ,\nwhere\n[math] is the identity\ncomponent of\n WG(K)\n= NG(K)∕K .