In  work  related  with  Positive  scalar  Curvature, Stephan Stolz (ann.of  Math),  but  later  Stolz-Kreck(HP  2 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?