  In this paper, we explore whether or not quark deconfinement may occur in
high-mass neutron stars such as J1614-2230 (1.97 \pm 0.04 M_Sun) and J0348+0432
(2.01 \pm 0.04 M_Sun). Our study is based on a non-local extension of the SU(3)
Nambu Jona-Lasinio (n3NJL) model with repulsive vector interactions among the
quarks. This model goes beyond the frequently used local version of the Nambu
Jona-Lasinio (NJL) model by accounting for several key features of QCD which
are not part of the local model. Confined hadronic matter is treated in the
framework of non-linear relativistic mean field theory. We find that both the
local as well as the non-local NJL model predict the existence of extended
regions of mixed quark-hadron (quark-hybrid) matter in high-mass neutron stars
with masses of 2.1 to 2.4 M_Sun. Pure quark matter in the cores of neutron
stars is obtained for certain parametrizations of the hadronic lagrangian and
choices of the vector repulsion among quarks. The radii of high-mass neutron
stars with quark-hybrid matter and/or pure quark matter cores in their centers
are found to lie in the canonical range of 12 to 13 km.
