Some duality properties for induced representations of enveloping algebras involve the character Trad g . We extend them to deformation Hopf algebras A h of a noetherian Hopf k-algebra A 0 satisfying Ext In the case of quantized enveloping algebras, this character lifts the character Trad g . We also prove Poincaré duality for such deformation Hopf algebras in the case where k [[h]] is an A h -module of finite projective dimension. We explain the relation of our construction with quantum duality. MSC2000: primary 16S80, 16W70; secondary 16D20.