Let $X$ be a smooth projective toric variety over $\mathbb{C}$. Is there a good presentation for the K-theory ring $K_0(X)$ in terms of the corresponding fan, analogous to the presentation of the Chow ring of $X$ as a quotient of the Stanley-Reisner ring?
By the Chern isomorphism, it should become isomorphic to the Stanley-Reisner ring over $\mathbb{Q}$, but I am interested in integral coefficients.
