We first review our application of the twist-induced star-deformation procedure to second quantization on a noncommutative space(time).The procedure deforms,in a coordinated way,the space(time) algebra and its symmetries,the wave-mechanical description of a system of n bosons/fermions,the algebra of creation and annihilation operators and also the commutation relations of the latter with functions of spacetime; our key requirement is the mode-decomposition independence of the quantum field.We then point out that the correct way to describe "finite" space-time transformations is based on the coaction of the (deformed) Hopf algebra H of functions on the group G of space(time) symmetries,rather than the action of the Hopf algebra H,dual to H,deformation of the Universal Enveloping Algebra of Lie(G).The noncommutativity of H,i.e.of the parameters of a change of reference frames,hints at the quantum nature of the latter.We finally discuss the case of the quantum theory of a scalar field on a Groenewold-Moyal-Weyl noncommutative space(time).