  For each invariant polynomial $\Phi$, we construct a global CR invariant via
the renormalized characteristic form of the Cheng--Yau metric on a strictly
pseudoconvex domain. When the degree of $\Phi$ is 0, the invariant agrees with
the total $Q'$-curvature. When the degree is equal to the CR dimension, we
construct a primed pseudo-hermitian invariant $\mathcal{I}'_\Phi$ which
integrates to the corresponding CR invariant. These are generalizations of the
$\mathcal{I}'$-curvature on CR five-manifolds, introduced by Case--Gover.
