  The Nambu--Jona-Lasinio (NJL) - Jet model provides a sound framework for
calculating the fragmentation functions in an effective chiral quark theory,
where the momentum and isospin sum rules are satisfied without the introduction
of ad hoc parameters. Earlier studies of the pion fragmentation functions using
the NJL model within this framework showed qualitative agreement with the
empirical parameterizations. Here we extend the NJL-Jet model by including the
strange quark. The corrections to the pion fragmentation functions and
corresponding kaon fragmentation functions are calculated using the elementary
quark to quark-meson fragmentation functions from NJL. The results for the kaon
fragmentation functions exhibit a qualitative agreement with the empirical
parameterizations, while the unfavored strange quark fragmentation to pions is
shown to be of the same order of magnitude as the unfavored light quark's. The
results of these studies are expected to provide important guidance for the
analysis of a large variety of semi-inclusive data.
