The eta invariant and the real connective K-theory of the classifying   space for quaternion groups
  We express the real connective $K$ theory groups of the quaternion QL group of order $2^j\ge8$ in terms of the representation theory of by showing $ko_{4k-1}(BQL)=KSp(S^{4k+3}/\tau QL)$ where $tau$ is any fixed point free representation of QL in U(2k+2) 
E. Barrera-Yanez and P. Gilkey