  Let p be a prime and q=p^g. We show that the Grothendieck ring of finitely
generated F_{q}[SL(2,F_{q})]-modules is naturally isomorphic to the quotient of
the polynomial algebra Z[x] by the ideal generated by f^[g](x)-x, where
f(x)=sum_{j=0}^{floor(p/2)}(-1)^{j}(p/(p-j))((p-j); j)x^{p-2j}, and the
superscript [g] denotes g-fold composition of polynomials. We conjecture that a
similar result holds for simply connected semisimple algebraic groups defined
and split over a finite field.
