  A possible feature of the inert doublet model (IDM) is to provide a dark
matter candidate together with an alteration of both direct and indirect
collider constraints that allow for a heavy Higgs boson. We study the IDM in
light of recent results from Higgs searches at the Large Hadron Collider (LHC)
in combination with dark matter direct detection limits from the XENON
experiment. We ask under what conditions the IDM can still accommodate a heavy
Higgs boson. We find that IDM scenarios with a Higgs boson in the mass range
160-600 GeV are ruled out only when all experimental constraints are combined.
For models explaining only a fraction of the dark matter the limits are
weakened, and IDMs with a heavy Higgs are allowed. We discuss the prospects for
future detection of such IDM scenarios in the four-lepton plus missing energy
channel at the LHC. This signal can show up in the first year of running at
\sqrt{s} = 14 TeV, and we present detector-level studies for a few benchmark
models.
