  We study the coarse Baum-Connes conjecture for product spaces and product
groups. We show that a product of CAT(0) groups, polycyclic groups and
relatively hyperbolic groups which satisfy some assumptions on peripheral
subgroups, satisfies the coarse Baum-Connes conjecture. For this purpose, we
construct and analyze an appropriate compactification and its boundary,
"corona", of a product of proper metric spaces.
