  Electroweak precision measurements indicate that the standard model Higgs
boson is light and that it could have already been discovered at LEP 2, or
might be found at the Tevatron Run 2. In the context of a TeV^-1 size extra
dimensional model, we argue that the Higgs boson production rates at LEP and
the Tevatron are suppressed, while they might be enhanced at the LHC or at
CLIC. This is due to the possible mixing between brane and bulk components of
the Higgs boson, that is, the non-trivial brane-bulk `location' of the lightest
Higgs. To parametrize this mixing, we consider two Higgs doublets, one confined
to the usual space dimensions and the other propagating in the bulk.
Calculating the production and decay rates for the lightest Higgs boson, we
find that compared to the standard model (SM), the cross section receives a
suppression well below but an enhancement close to and above the
compactification scale M_c. This impacts the discovery of the lightest (SM
like) Higgs boson at colliders. To find a Higgs signal in this model at the
Tevatron Run 2 or at the LC with sqrt(s)=1.5 TeV, a higher luminosity would be
required than in the SM case. Meanwhile, at the LHC or at CLIC with sqrt(s) ~
3-5 TeV one might find highly enhanced production rates. This will enable the
latter experiments to distinguish between the extra dimensional and the SM for
M_c up to about 6 TeV.
