Rational G-spectra with Weyl-finite isotropy

For a compact Lie group G, we may study G-equivariant cohomology theories, and it is conjectured that there is an abelian category A(G) so that there is an equivalence between rational G-spectra  =  dg A(G).
The category A(G) is (in a sense to be made precise) a category of sheaves over the space X(G) of conjugacy classes of subgroups of G. In fact X(G) is a finite disjoint union of blocks V(G,H) (where H is a subgroup with finite Weyl group) so A(G)=A(V(G,H1)) x  …… x A(V(G,Hn)).

The talk will describe some progress understanding the structure of blocks in general and explain the algebraic model  A(V(G,H)) for Weyl-finite blocks V(G,H). More generally it will describe the category of rational G-spectra with any specified Weyl-finite geometric isotropy.