For relative K-groups of truncated polynomial algebras and relation to topological Hochschild homology, see http://www.math.uiuc.edu/K-theory/0162
Goodwillie: Relative algebraic K-theory and cyclic homology (1986)
McCarthy: Relative algebraic K-theory and topological cyclic homology (1997)
arXiv: Experimental full text search
KT (K-theory), AG (Algebraic geometry)?, NCG (Algebra and noncommutative geometry)?
nLab page on Relative K-theory