In work related to positive scalar curvature, Stephan Stolz (Ann. 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?