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