We report results on the adsorbate-adsorbent system CO2-nontronite at 230¿K, 196¿K, 158¿K, covering the range of subsurface regolith temperature on Mars. These results, together with Viking observations have allowed construction of a three-part regolith-atmosphere-cap model describing storage and exchange of atmosphere-exchangeable CO2. Cold nontronite, and 'expanding' clays in general, are far better adsorbers for CO2 than cold pulverized basalt and exhibit far more complex adsorptive properties as well. Both observations result from a limitation on interlayer H2O content of clays at low temperature (even when the humidity is high). This makes available energeticaly favorable adsorption sites for CO2 and creates a micropore structure allowing capillary condensation of CO2 at Martian near-polar temperatures. The layered terrain, and possibly the adjacent debris mantle, contains ~2% or more by mass of atmosphere-exchangeable CO2(~12 cc STP/g) and the total regolith inventory of available adsorbed CO2 is estimated to be ?6¿1020 g or 4¿102 g/cm2 as a global average. Thus the 'ocean' of adsorbed CO2 in the regolith, not the atmosphere or surface caps, is the main repository of atmosphere-exchangeable CO2. Such a large near-polar subsurface reservoir of CO2 at relatively constant temperature can, either directly or via a small quasi-permanent cap, buffer the atmospheric CO2 pressure on a long-term basis while allowing annual caps to form in response to the wide seasonal variations in surface temperature. For example, isothermal removal (or addition) of atmospheric CO2 causes the large regolith buffer to contribute (or adsorb) atmospheric CO2 in response. Thermal changes also cause important buffering responses. The best understood of these is the obliquity variation,which can produce a ~15¿ increase or decrease in near-polar temperatures relative to present values. An increase would produce rapid dissipation of any quasi-permanent CO2 cap and then the regolith would buffer pressures which could rise to ~20 mb. A decrease would give rise to a situation in which the cap would buffer the pressure as it falls to a minimum of <1 mb. As the pressure falls, the regolith probably transfers much larger amounts of CO2 to the growing cap than the cap would acquire from the atmosphere. The predicted variation in atmospheric pressure (greater than a factor of 10 independent of postulates concerning the existence of a massive surface CO2 reservoir) together with the predicted periodic variations in cap size may have helped generate the layered terrain and other surface features. Also the predicted periodic 'flushing' of the atmosphere resulting from regolith-cap CO2 transfer can explain the near absence of 18O enrichment in the atmosphere observed by the Viking probe mass spectrometer, while other aspects of the model are consistent with and help to explain certain of the Viking lander gas chromatograph-mass spectrometer (GCMS) and gas exchange experiment (GEX) gas evolution observations.