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We use Grayson's binary multicomplex presentation of algebraic $K$-theory togive a new construction of exterior power operations on the higher $K$-groupsof a (quasi-compact) scheme. We show that these operations satisfy the axiomsof a $\lambda$-ring, including the product and composition laws. To prove thecomposition law we show that the Grothendieck group of the exact category ofintegral polynomial functors is the universal $\lambda$-ring on one generator.

Exterior power operations on higher $K$-groups via binary complexes