The Deligne-Mumford-Knudsen moduli space of n-pointed stable curves of genus 0 is a smooth projective variety of dimension n - 3. We construct an integral isomorphism from its Grothendieck ring of vector bundles to its Chow cohomology ring which satisfies a Hirzebruch-Riemann-Roch-type formula. This isomorphism, which is unrelated to the Chern character, can be used to reduce many K-theoretic computations to easier problems in intersection theory. Joint with Shiyue Li, Sam Payne, and Nick Proudfoot.