  When the anti-periodic boundary condition is imposed for a bulk field in
extradimensional theories, independently of the background metric, the lightest
component in the anti-periodic field becomes stable and hence a good candidate
for the dark matter in the effective 4D theory due to the remaining accidental
discrete symmetry. Noting that in the gauge-Higgs unification scenario,
introduction of anti-periodic fermions is well-motivated by a phenomenological
reason, we investigate dark matter physics in the scenario. As an example, we
consider a five-dimensional SO(5)$\timesU(1)_X$ gauge-Higgs unification model
compactified on the $S^1/Z_2$ with the warped metric. Due to the structure of
the gauge-Higgs unification, interactions between the dark matter particle and
the Standard Model particles are largely controlled by the gauge symmetry, and
hence the model has a strong predictive power for the dark matter physics.
Evaluating the dark matter relic abundance, we identify a parameter region
consistent with the current observations. Furthermore, we calculate the elastic
scattering cross section between the dark matter particle and nucleon and find
that a part of the parameter region is already excluded by the current
experimental results for the direct dark matter search and most of the region
will be explored in future experiments.
