We present a quantitative model for atmosphere-regolith exchange of CO2 on Mars based on new laboratory measurements of CO2 adsorption on ground rock at temperatures of 158¿, 175¿, 196¿, and 231¿K and CO2 pressures from 1.0 to 80 mbar. Our model is consistent with Viking observations, whereas models involving a massive residual CO2 cap and no long-term atmosphere-regolith CO2 exchange are not. Our model describes the role of the regolith as a CO2 storehouse, as a long-term buffer of the atmospheric pressure, and as a mojor factor in determining the response of the atmosphere to postulated changes in surface insolation. We conclude the following: (1) The atmosphere-plus-cap system is buffered on a long-term basis by several hundred grams per square centimeter of exchangeable CO2 adsorbed in the regolith. (2) If the atmosphere-plus-cap system were arbitrarily removed in its entirety, it would eventually be restored to nearly its former state by reequilibration with the regolith. (3) Exchange with the absorbed phase in the regolith has greatly restricted 18O enrichment in the atmosphere. (4) The layered terrain primarily represents current periodic pressure increases (of several tens of millibars) caused by exchange of CO2 between the regolith and the atmosphere-plus-cap system. (5) Pressures of 100--300 mbar might have existed during the early history of the planet.