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We construct an abelian category A(G) of sheaves over a category of closedsubgroups of the r-torus G and show it is of finite injective dimension. It canbe used as a model for rational $G$-spectra in the sense that there is ahomology theory  \piA_*: G-spectra/Q --> A(G) on rational G-spectra with values in A(G), andthe associated Adams spectral sequence converges for all rational $G$-spectraand collapses at a finite stage.

Rational torus-equivariant homotopy I: calculating groups of stable maps