The fundamental theorem via derived Morita invariance, localization, and   A^1-homotopy invariance
  We prove that every functor defined on dg categories, which is derived Morita invariant, localizing, and A^1-homotopy invariant, satisfies the fundamental theorem. As an application, we recover in a unified and conceptual way, Weibel and Kassel's fundamental theorems in homotopy algebraic K-theory, and periodic cyclic homology, respectively. 
Goncalo Tabuada
math.KT math.AG math.AT