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