  A Higgs-like resonance with a mass of approximately 750 GeV has recently been
observed at the LHC in its diphoton decay. If this state is not simply a
statistical fluctuation which will disappear with more data, it will have
important implications not only for particle physics but also for cosmology. In
this note, we analyze the implications of such a resonance for the dark matter
(DM). Assuming a spin 1/2 DM particle, we first verify that indeed the correct
relic density can be obtain for a wide range of the particle mass and weak
scale coupling that are compatible with present data. We then show that the
combination of near future direct and indirect detection experiments will allow
to probe the CP-nature of the mediator resonance, i.e. check whether it is a
scalar or a pseudoscalar like particle.
