Equivariant categorification of the quantum orthogonal algebra

Let $m\geq 2$, let $U'_{-q^2}(\mathfrak{so}_{m})$ be the quantum orthogonal algebra with elements $\mathsf{x}_i^{(k)}$, and let ${\EuScript B}_{m}$ be the relevant monoidal category with involution $\tau$. Equivariant categorification conjecture. There is an isomorphism of ${\mathbb C}(q)$-algebras

$$U'_{-q^2}(\mathfrak{so}_{m})\xrightarrow{\cong}{\mathbb C}(q)\otimes_{{\mathbb Z}[q^\pm]}K_0^\tau(( {\EuScript B}_{m})^\tau)$$

that sends $\mathsf{x}_i^{(k)}$ to the class of an appropriate equivariant structure on $\mathbf X_i^{(k)}=\mathcal F_i^{(k)}\mathcal E_i^{(k)}\mathbbm1_{\mathbf n}$. The $m=2$ case is proved in the paper; the assertion extends that categorification to all $m\geq2$.