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In this paper we revisit the model of $\kappa$-deformed complex scalar field.We find that this model possesses ten conserved Noether charges that form,under commutators, a representation of (undeformed) Poincar\'e algebra. Itfollows that the theory is relativistic and does not break Lorentz invariance.However the spacetime representation of boosts is not standard, and contains anon-local translation, different for positive and negative energy modes. Itthen follows that although the masses of particles and anti-particles areequal, the theory violates CPT symmetry in a subtle way. We explain why theJost-Wightman-Greenberg theorem of equivalence of the Poincar\'e symmetry andCPT fails in our case. Finally, we discuss the phenomenological consequences ofthe theory and its possible observational signatures.

$\kappa$-deformed complex scalar field: conserved charges, symmetries and their impact on physical observables