  We establish the quenched local limit theorem for reversible random walk on
$\Z^d$ (with $d\ge 2$) among stationary ergodic random conductances that permit
jumps of arbitrary length. The proof is based on the weak parabolic Harnack
inequalities and on-diagonal heat-kernel estimates for long-range random walks
on general ergodic environments. In particular, this partly solves \cite[Open
Problem 2.7]{BCKW}, where the quenched invariance principle was obtained. As a
byproduct, we prove the maximal inequality with an extra tail term for
long-range reversible random walks, which in turn yields the everywhere
sublinear property for the associated corrector.
