Strong Chow pushforward conjecture for properly stable smooth Artin stacks

Let $\pi\colon\mathcal {X}\to{\mathbf X}$ be a good moduli space map, where $\mathcal {X}$ is a properly stable smooth Artin stack. For a strong cycle $\mathcal {Z}$, let $e_\mathcal {Z}$ denote its generic stabilizer order. Strong Chow pushforward conjecture. The assignment

$$[\mathcal {Z}]\longmapsto e_\mathcal {Z}^{-1}[\pi(\mathcal {Z})]$$

respects rational equivalence and therefore induces a pushforward map

$$\pi_{st,*}\colon A^k_{st}(\mathcal {X}/{\mathbf X})_\mathbb{Q}\to A^k({\mathbf X})_\mathbb{Q}.$$

This conjecture proposes a functorial pushforward on the subgroup generated by strong cycles, avoiding the failure of a pushforward on the full Chow ring for arbitrary regular embeddings.