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We show that the fundamental class in K-homology of a Frobenius split schemecan be computed as a certain alternating sum over irreducible varieties, withthe coefficients computed using M\"obius inversion on a certain poset. If G/Pis a generalized flag manifold and X is an irreducible subvariety homologous toa multiplicity-free union of Schubert varieties, then using a result of Brionwe show how to compute the K_0-class [X] in K_0(G/P) from the Chow class inA_*(G/P).

Frobenius splitting and M\"obius inversion