(note: excerpt from: MIT Center for Global Change Science)
Focus on Upper Atmospheric Chemistry and Circulation
Theoretical studies of the greenhouse effect indicate that a rise in the level of the greenhouse gases will tend not only to warm the Earth's surface and the lower atmosphere but also to cool the stratosphere.
This cooling of the stratosphere is expected to affect the ozone layer by decreasing ozone destruction in equatorial regions and increasing ozone destruction in polar regions. (image right from Metoffice.gov.UK)
These effects would be added to the increased ozone destruction expected due to rising chlorofluorocarbon concentrations.
The stratospheric cooling by the greenhouse gases combined with these ozone layer changes will in turn affect the circulation at this level and conceivably at lower levels also.
Indeed, there is already some evidence that Antarctic ozone changes have been influencing the Southern Hemisphere springtime climate by delaying the final warming.