  By analogy with the classical construction due to Forrest, Samei and Spronk
we associate to every compact quantum group $\mathbb{G}$ a completely
contractive Banach algebra $A_\Delta(\mathbb{G})$, which can be viewed as a
deformed Fourier algebra of $\mathbb{G}$. To motivate the construction we first
analyse in detail the quantum version of the integration over the diagonal
subgroup, showing that although the quantum diagonal subgroups in fact never
exist, as noted earlier by Kasprzak and So{\l}tan, the corresponding
integration represented by a certain idempotent state on $C(\mathbb{G})$ makes
sense as long as $\mathbb{G}$ is of Kac type. Finally we analyse as an explicit
example the algebras $A_\Delta(O_N^+)$, $N\ge 2$, associated to Wang's free
orthogonal groups, and show that they are not operator weakly amenable.
