In this paper (arXiv:1402.2884) we show that the Drinfel’d double associated to the standard quantum deformation of sl(2,R) is isomorphic to the (2+1)-dimensional AdS algebra with the initial deformation parameter η related to the cosmological constant Λ. This gives rise to a generalisation of a non-commutative Minkowski spacetime that arises as a consequence of the quantum double symmetry of (2+1) gravity to non-vanishing cosmological constant. The properties of the AdS quantum double that generalises this symmetry to the case Λ≠0 are sketched, and it is shown that the new non-commutative AdS spacetime is a nonlinear Λ-deformation of the Minkowskian one.