The Steinberg torus is a cell complex naturally associated to any affine Weyl group W. Although less well known than the Coxeter complex, it deserves equal billing in the affine Coxeter world. In this talk we will survey some of the interesting applications of this object, including (1) Steinberg's slick proof of Bott's formula for the Poincare series of W, and (2) some recent joint work with K. Petersen and K. Dilks on the combinatorics of affine descents.

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