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

An Explicit Presentation of the Grothendieck Ring of Finitely Generated F_{q}[SL(2,F_{q})]-Modules