  We investigate the properties of kappa-Minkowski spacetime by using
representations of the corresponding deformed algebra in terms of undeformed
Heisenberg-Weyl algebra. The deformed algebra consists of kappa-Poincare
algebra extended with the generators of the deformed Weyl algebra. The part of
deformed algebra, generated by rotation, boost and momentum generators, is
described by the Hopf algebra structure. The approach used in our
considerations is completely Lorentz covariant. We further use an adventages of
this approach to consistently construct a star product which has a property
that under integration sign it can be replaced by a standard pointwise
multiplication, a property that was since known to hold for Moyal, but not also
for kappa-Minkowski spacetime. This star product also has generalized trace and
cyclic properties and the construction alone is accomplished by considering a
classical Dirac operator representation of deformed algebra and by requiring it
to be hermitian. We find that the obtained star product is not translationally
invariant, leading to a conclusion that the classical Dirac operator
representation is the one where translation invariance cannot simultaneously be
implemented along with hermiticity. However, due to the integral property
satisfied by the star product, noncommutative free scalar field theory does not
have a problem with translation symmetry breaking and can be shown to reduce to
an ordinary free scalar field theory without nonlocal features and tachionic
modes and basicaly of the very same form. The issue of Lorentz invariance of
the theory is also discussed.
