  In this paper we recall the construction of scalar field action on
$\kappa$-Minkowski space-time and investigate its properties. In particular we
show how the co-product of $\kappa$-Poincar\'e algebra of symmetries arises
from the analysis of the symmetries of the action, expressed in terms of
Fourier transformed fields. We also derive the action on commuting space-time,
equivalent to the original one. Adding the self-interaction $\Phi^4$ term we
investigate the modified conservation laws. We show that the local interactions
on $\kappa$-Minkowski space-time give rise to 6 inequivalent ways in which
energy and momentum can be conserved at four-point vertex. We discuss the
relevance of these results for Doubly Special Relativity.
