In work related with positive scalar curvature, *Stephan Stolz (ann.of Math)*, but later  *Stolz-Kreck*($HP2$ bundles  and Elliptic cohomology) introduced a version of Real connective  $K$-homology by considering spin cobordism, localizing at the prime $2$ and  then killing  classes which  are determined  by  bundles  with  fiber  $HP2$.  
Is  there  an  analogous  version  for  complex (connective) $K$-homology?