  We introduce a notion of equivariant coarse cohomology of the complement of a
subspace in a metric space. We use this cohomology to define a notion of coarse
cohomology of the configuration space of a metric space and develop tools to
compute this cohomology under certain conditions. As an application of this
theory, we show that certain classes in the coarse cohomology of configuration
space obstruct coarse embedding between two metric spaces.
