Strong Chow ring conjecture for properly stable smooth Artin stacks

Let $\mathcal {X}$ be a properly stable smooth Artin stack with good moduli space ${\mathbf X}$. The strong relative Chow groups $A^k_{st}(\mathcal {X}/{\mathbf X})$ are generated by strong cycles. Strong Chow ring conjecture. The graded group

$$\bigoplus_{k=0}^{\dim \mathcal {X}} A^k_{st}(\mathcal {X}/{\mathbf X})$$

is a subring of $A^*(\mathcal {X})$ under the intersection product. This is posed as a conjectural answer to whether strong cycles are closed under intersection products.