  In this paper, we construct new models for the Anderson duals $(I\Omega^G)^*$
to the stable tangential $G$-bordism theories and their differential
extensions. The cohomology theory $(I\Omega^G)^*$ is conjectured by Freed and
Hopkins [FH21] to classify deformation classes of possibly non-topological
invertible quantum field theories (QFT's). Our model is made by abstractizing
certain properties of invertible QFT's, thus supporting their conjecture.
