Abstract: For an algebraic variety X over an arbitrary field F, a classical question asks whether X has a K-point for a given field extension K/F. When X is a generalized Severi-Brauer variety, we may extend this question to ask not only about K-points, but about K-forms of any closed Schubert subvariety. In this talk, we consider an algebraic form of this question concerning data from the underlying central simple algebra of X. We then discuss applications to the Grothendieck group and Chow group of X, generalizing a result of N. Karpenko for usual Severi-Brauer varieties. This is part of ongoing work with D. Krashen and N. Lemire.