“For X a smooth quasi-projective variety, there are natural Chern class maps from the semi-topological K-groups of X to its morphic cohomology groups compatible with similarly defined Chern class maps from algebraic K-theory to motivic cohomology and compatible with the classical Chern class maps from topological K-theory to the singular cohomology of X.”
Friedlander and Walker: http://www.math.uiuc.edu/K-theory/0393, http://www.math.uiuc.edu/K-theory/0361, http://www.math.uiuc.edu/K-theory/0453, http://www.math.uiuc.edu/K-theory/0557 (looks interesting)
Techniques, Computations, and Conjectures for Semi-Topological K-theory, by Eric M. Friedlander, Christian Haesemeyer, and Mark E. Walker: http://www.math.uiuc.edu/K-theory/0621
arXiv: Experimental full text search
KT (K-theory), AG (Algebraic geometry)
Mixed
nLab page on Semi-topological K-theory