Dual coaction duality for exotic crossed products

Let $(B,\alpha)$ be an action of a locally compact group $G$ on a $C^*$-algebra $B$, and let $B\rtimes_{\alpha,E}G$ be its $E$-crossed product. Denote by $\hat\alpha_E$ the dual coaction on this exotic crossed product. Exotic dual-coaction conjecture. The dual coaction $\hat\alpha_E$ satisfies $E$-crossed-product duality. This is a structural compatibility conjecture for the exotic crossed-product construction; the supplied text gives no resolution.