ZAU Controller described a loss of separation event when the D-Side Controller made a control decision with another sector without receiving approval from the RADAR Controller.

Narrative

Aircraft X was inbound to GRB at FL260 descending to FL250; direct GRB. Aircraft Y was an ORD departure climbing initially to FL290 routed PECOK and Northeast bound into ZMP. I had descended Aircraft X to FL250 on top of a MKE inbound aircraft who was descending out of FL240. Aircraft Y was flashed late climbing to FL290 by Sector 60 who then called my D-Side to coordinate climbing to FL240 only underneath Aircraft X. My D-Side decided that instead of maintaining altitude separation; to have Sector 60 continue the climb of Aircraft Y and we would descend Aircraft X. I would never have approved that plan of action; but the decision was made for me. Sector 60 then proceeded to climb Aircraft Y and my D-Side got lower for Aircraft X who I then descended to 14000ft. I then turned Aircraft X; 15 right to try to get separation from Aircraft Y who was only out of FL210 and climbing. I was not talking to Aircraft Y. Sector 60 then proceeded to turn Aircraft Y 10 right which ended up putting the two aircraft more in conflict than before and still would not ship me Aircraft Y. I then turned Aircraft X to a 360 heading and told him to expedite all the way down. Aircraft Y was finally shipped and I told him to expedite up and to turn to a 90 heading. There was probably no more than 5.5 or 6 miles between the two aircraft at the same altitude. The D-Side should never have made that kind of control decision without asking me or letting me know what was going on before allowing Sector 60 to climb Aircraft Y into Aircraft X. The 2 aircraft should have been established on headings for separation before climbing Aircraft Y and descending Aircraft X. Sector 60 should never have attempted to separate aircraft in my airspace and should have shipped Aircraft Y to me in time for me to correct the heading and ensure separation. Coordination was poor in this case as was the decision-making of my D-Side.