Modified noncommutative Borsuk–Ulam conjecture of type II

Let $A$ be a unital C*-algebra equipped with a free action of a non-trivial compact quantum group $(H,\Delta)$, and let $A\circledast^\delta H$ be the equivariant noncommutative join C*-algebra of $A$ and $H$ with the induced free action of $(H,\Delta)$. Assume that $A$ admits a character. Modified noncommutative Borsuk–Ulam conjecture of type II. There does not exist an $(H,\Delta)$-equivariant $*$-homomorphism

$$H\longrightarrow A\circledast^\delta H.$$

Equivalently, the compact quantum principal bundle given by $A\circledast^\delta H$ is not trivializable. The paper presents this as a corollary of the type-I conjecture; the original type-II conjecture has counterexamples, so the character hypothesis is essential to this modified formulation.