The coarse Baum-Connes conjecture asserts that the higher index map from the coarse K-homology of a metric space X to the K-theory of the Roe algebra of X is an isomorphism. The conjecture has its roots in the celebrated Atiyah-Singer index theorem and has significant applications to topology and geometry, such as the Novikov conjecture and Gromov-Lawson-Rosenberg conjecture. A natural question is whether the conjecture is closed under products. In this talk, we will answer this   question by introducing a notion called the Roe algebra with filtered coefficients which is inspired by Yu’s quantitative K-theory.