Loop structures on the homotopy type of S^3 revisited
  We observe that the Rector invariants classifying the genus of BS^3 show up in (orthogonal and unitary) K-theory. We then use this knowledge to show purely algebraically how the K-theory of the spaces in the genus of BS^3 differ. This provides new insights into a result of Notbohm in the case of BS^3. 
Donald Yau