compatible with the deformation, i.e. with the twisted symmetry algebra. This means that $[\Delta (\Lambda), \tau] = 0.$ The symmetry algebra that admits the existence of such flip operator belongs to a class of bialgebras that possess a quasitriangular structure, which means that a universal quantum $R$-matrix for such symmetry algebras can be found. We recall that $R$-matrix for the symmetry algebra $\mathfrak{G}$ is an invertible element $R \in
\mathfrak{G} \otimes  \mathfrak{G} $ having the property $$R \Delta (\Lambda) R^{-1} = \tilde{\Delta} (\Lambda),$$ for all $\Lambda \in \mathfrak{G}. $ Here $\tilde{\Delta} (\Lambda)$ is the opposite coproduct of $\Delta (\Lambda),$ where the factors in the tensor product are interchanged in every term. In this case the statistics flip operator $\tau$ can be expressed as $\tau = \tau_0 R,$ where $\tau_0 $ is the undeformed flip operator, $\tau_0 (| \phi_1 \rangle \otimes |
\phi_2 \rangle) = | \phi_2 \rangle \otimes | \phi_1 \rangle,$ for any $| \phi_1 \rangle, | \phi_2 \rangle \in V. $

We believe that the further detailed study of the algebraic structure of $\kappa$-Poincaré, in particularly the study of its triangular quasibialgebra structure is of high importance. The existence of the triangular quasibialgebra structure ensures that there is a 