  We propose the notion of a coarse cohomology theory and study the examples of
coarse ordinary cohomology, coarse stable cohomotopy and of coarse cohomology
theories obtained by dualizing coarse homology theories. We show that the
dualizing spectrum of a finitely generated torsion-free group only depends on
the coarse motivic spectrum represented by the underlying bornological coarse
space of the group. This in particular implies a conjecture of J. R. Klein that
the dualizing spectrum of a group is a coarse invariant.
