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We prove in this paper a Borel-Weil-Bott type theorem for the coHochschildhomology of a quantum shuffle algebra associated with quantum group datumtaking coefficients in some well-chosen bicomodules, which can be looked as ananalogue of equivariant line bundles over flag varieties in the non-commutativecase.

A Borel-Weil-Bott type theorem of quantum shuffle algebras