  A description of fragmentation functions which satisfy the momentum and
isospin sum rules is presented in an effective quark theory. Concentrating on
the pion fragmentation function, we first explain why the elementary (lowest
order) fragmentation process q --> q \pi is completely inadequate to describe
the empirical data, although the "crossed" process \pi --> q \bar{q} describes
the quark distribution functions in the pion reasonably well. Taking into
account cascade-like processes in a generalized jet-model approach, we then
show that the momentum and isospin sum rules can be satisfied naturally,
without the introduction of ad hoc parameters. We present results for the
Nambu--Jona-Lasinio (NJL) model in the invariant mass regularization scheme and
compare them with the empirical parametrizations. We argue that the NJL-jet
model, developed herein, provides a useful framework with which to calculate
the fragmentation functions in an effective chiral quark theory.
