  The main result of this paper is the computation of TR^n_{\alpha}(F_p;p) for
\alpha in R(S^1). These R(S^1)-graded TR-groups are the equivariant homotopy
groups naturally associated to the S^1-spectrum THH(F_p), the topological
Hochschild S^1-spectrum. This computation, which extends a partial result of
Hesselholt and Madsen, provides the first example of the R(S^1)-graded
TR-groups of a ring. These groups arise in algebraic K-theory computations, and
are particularly important to the understanding of the algebraic K-theory of
non-regular schemes.
