An algebraic model for rational G-spectra over an exceptional subgroup

We give a simple algebraic model for rational G-spectra over an exceptional subgroup, for any compact Lie group G. Moreover, all our Quillen equivalences are symmetric monoidal, so as a corollary we obtain a monoidal algebraic model for rational G-spectra when G is finite. We also present a study of the relationship between induction - restriction - coinduction adjunctions and left Bousfield localizations at idempotents of the rational Burnside ring.