  We discuss the obstruction to the construction of a multiparticle field
theory on a $\kappa$-Minkowski noncommutative spacetime: the existence of
multilocal functions which respect the deformed symmetries of the problem. This
construction is only possible for a light-like version of the commutation
relations, if one requires invariance of the tensor product algebra under the
coaction of the $\kappa$-Poincar\'e group. This necessitates a braided tensor
product. We study the representations of this product, and prove that
$\kappa$-Poincar\'e-invariant N-point functions belong to an Abelian
subalgebra, and are therefore commutative. We use this construction to define
the 2-point Whightman and Pauli--Jordan functions, which turn out to be
identical to the undeformed ones. We finally outline how to construct a free
scalar $\kappa$-Poincar\'e-invariant quantum field theory, and identify some
open problems.
