Conjecture that the involution of the Grothendieck ring is a group automorphism

Let $\mathfrak{r}$ be the group equipped with the involution $d$. The group-automorphism conjecture. The involution $d$ of $\mathfrak{r}$ is a group automorphism. This is proposed as a generalization of the preceding result, whose proof applies only when the multiplication map is bijective; the conjecture asserts that the same conclusion holds more generally.