We exhibit an appropriate suspension of bounded flag manifolds as a wedge sum of Thom complexes of associated complex line bundles. We use the existence of such a splitting to assist our computation of real and complex K-groups. Moreover, we compute the Sq^2-homology of bounded flag manifolds to make use of relevant Atiyah-Hirzebruch spectral sequence of KO-theory.
CİVAN, YUSUF (2002) "KO-groups of Bounded Flag Manifolds," Turkish Journal of Mathematics: Vol. 26: No. 4, Article 6. Available at: https://journals.tubitak.gov.tr/math/vol26/iss4/6