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Let K 0 (Fp GLn(Fp)-proj) denote the Grothendieck group of finitely generatedpro-jective Fp GLn(Fp)-modules. We show that the algebra C $\otimes$ n$\ge$0 K0 (Fp GLn(Fp)-proj) with multiplication given by induction functors, is apolynomial algebra. We explicit generators and their relation withDeligne-Lusztig characters.

Polynomiality of Grothendieck groups for finite general linear groups, Deligne-Lusztig characters, and injective unstable modules