Quantitative K-theory and the K{\"u}nneth formula for operator algebras
  In this paper, we apply quantitative operator K-theory to develop an algorithm for computing K-theory for the class of filtered C *-algebras with asymptotic finite nuclear decomposition. As a consequence, we prove the K{\"u}nneth formula for C *-algebras in this class. Our main technical tool is a quantitative Mayer-Vietoris sequence for K-theory of filtered C *-algebras. 
Herv\'e Oyono-Oyono, Guoliang Yu
math.OA