That cross piece (2x2 ?) obviously isn't carrying the joist so you need to remove the insulation to see where, behind the red wall, the joist support point is and then determine just how extensive the split is.
If there is room once you have removed that insulation, I would think a simple repair by spanning the crack on either side with fresh wood bolted through the existing joist would suffice.
Is it possible to get another pic with the insulation removed, showing the extent of the crack?
It may well be no problem structurally, but it depends on how the crack runs.
I agree with garyo, looks more like a cut than a split, too uniform and no discoloration either side. But either or it's a simple enough job, just take out the bats of insulation in front and screw a steel plate both sides [i i.e.[/i] plate it. A couple of through bolts to the accessible parts if there's any movement wouldn't go amiss...pinenot
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