Abstract: The stellahedral toric variety is a toric variety whose cohomology ring and K-ring are both closely related to matroids. We construct an integral isomorphism from the K-ring to the cohomology ring of the stellahedral toric variety, and use this to prove that three equivalence relations on matroids, valuative equivalence, numerical equivalence, and homological equivalence, coincide. Based on joint work with Chris Eur and June Huh.