  We study a one-dimensional random walk among random conductances, with
unbounded jumps. Assuming the ergodicity of the collection of conductances and
a few other technical conditions (uniform ellipticity and polynomial bounds on
the tails of the jumps) we prove a quenched \textit{uniform} invariance
principle for the random walk. This means that the rescaled trajectory of
length $n$ is (in a certain sense) close enough to the Brownian motion,
uniformly with respect to the choice of the starting location in an interval of
length $O(\sqrt{n})$ around the origin.

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