Shang's character-formula conjecture for free alternative algebras

Let $V$ be a finite-dimensional vector space, let $\operatorname{Alt}(V)$ denote the free alternative algebra generated by $V$, and let $\mathcal{B}(\operatorname{Alt}(V))$ be the associated Allison--Benkart--Gao auxiliary space. Let $a(V)$ and $b(V)$ be the elements of the augmentation ideal of the Grothendieck ring of $GL(V)$ defined by the stated identities.

Shang's character-formula conjecture. In the Grothendieck ring of $GL(V)$,

$$[\operatorname{Alt}(V)]=a(V),\qquad [\mathcal{B}(\operatorname{Alt}(V))]=b(V).$$

According to the source, this conjecture is implied by Shang's homological conjecture, which the paper disproves; the source does not separately establish whether this character-formula conjecture itself is false.