Vector bundles of non-negative curvature over cohomogeneity one manifolds

We provide several results on the existence of metrics non-negative sectional curvature vector bundles over certain cohomogeneity one manifolds and homogeneous spaces up to suitable stabilization. Beside explicit constructions metrics, this is achieved by identifying equivariant structures upon these via a comparison their non-equivariant K-theory. For this, in particular, we transcribe K-theory rational cohomology investigate surjectivity properties induced maps Borel fibration homotopy theory.