J.P.C.Greenlees ``Rational torus-equivariant stable homotopy II: the algebra of localization and inflation.'' This is the second in a series designed to give a complete algebraic model for rational torus equivariant cohomology theories. It gives an algebraic study of the category A(G) for an r-torus G. The first main result is one which explains how global information can be reassembled from small sets of isotropy groups, and the second is to explain how A(G) can be viewed as a category of modules over a ring R with many objects. [The distribution of material between Part I and Part II has been substantially reorganized, to the great benefit of readability. However the mathematical content is unchanged (31/8/01).] (27/7/01; reorganized version 31/8/01)