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We study residue formulas for push-forward in K-theory of homogeneous spaces.First we review formulas for classical groups, which we derive from a formulafor the classical Grassmannian case. Next we consider the homogeneous spacesfor G2. One of them embeds in the Grassmannian Gr(2,7). We find its fundamentalclass in the equivariant K-theory and obtain the residue formula for thepush-forward. This formula is valid for G2/B as well.

Residues formulas for the push-forward in K-theory, the case of G2/P