  This paper is presented on the occasion of 60-th birthday of Jose Adolfo de
Azcarraga who in his very rich scientific curriculum vitae has also a chapter
devoted to studies of quantum-deformed symmetries, in particular deformations
of relativistic and Galilean space-time symmetries [1-4].
  In this paper we provide new steps toward describing the $\kappa$-deformed
D=4 conformal group transformations. We consider the quantization of D=4
conformal group with dimensionful deformation parameter $\kappa$. Firstly we
discuss the noncommutativity following from the Lie-Poisson structure described
by the light-cone $\kappa$-Poincar\'{e} $r$-matrix. We present complete set of
D=4 conformal Lie-Poisson brackets and discuss their quantization. Further we
define the light-cone $\kappa$-Poincar\'{e} quantum $R$-matrix in O(4,2) vector
representation and discuss the inclusion of noncommutative conformal
translations into the framework of $\kappa$-deformed conformal quantum group.
The problem with real structure of $\kappa$-deformed conformal group is pointed
out.
