Abstract
In this paper, we generalize the push-forward (Gysin) formulas for flag bundles in the ordinary cohomology theory, which are due to Darondeau-Pragacz, to the complex cobordism theory. Then we introduce the {\it universal quadratic Schur functions}, which are a generalization of the (ordinary) quadratic Schur functions introduced by Darondeau-Pragacz, and establish some Gysin formulas for the universal quadratic Schur functions as an application of our Gysin formulas.
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