On Grothendieck's Riemann-Roch theorem

We prove that, for smooth quasi-projective varieties over a field, the K-theory K(X) of vector bundles is the universal cohomology theory where c1(L⊗L̄)=c1(L)+c1(L̄)−c1(L)c1(L̄). Then, we show that Grothendieck's Riemann-Roch theorem is a direct consequence of this universal property, as well as the universal property of the graded K-theory GK
- (X)⊗Q.