The aircraft-based 2002 Intercontinental Transport and Chemical Transformation experiment intercepted and chemically analyzed pollution plumes transported from Asia to the western United States. The research flight on 10--11 May 2002 detected mixing between polluted and stratospheric air at midtropospheric levels above the California coast. This study uses a Lagrangian domain-filling trajectory technique to illustrate that this event was the result of mixing between two warm conveyor belts (WCB) containing Asian pollution and the remnants of a deep tropopause fold from a downstream midlatitude cyclone (referred to as the stratospheric component of a dry airstream or SCDA). Advection of the trajectory particles shows how the SCDA decayed over 7.5 days. One component dispersed into a downstream WCB, while another component descended into the lower troposphere and became entrained by an upwind WCB. After 7.5 days of transport 22% of the SCDA mass was transported into the troposphere. The portions of the SCDA that penetrated to the lowest altitudes had the greatest likelihood of being transported into the troposphere. For example, over 90% of the SCDA at altitudes below the 600 hPa level was transported to the troposphere, but none of the mass at the 200 hPa level was exchanged. More than half of the exchange occurred during the first 48 hours as the deepest portions of the tropopause fold decayed over the Pacific. The rest of the exchange occurred over the following 5.5 days as the remnants of the SCDA sheared apart along the edge of the stratospheric polar vortex and became entrained into subsequent tropopause folds and vortex breakaway features. Stratosphere to troposphere exchange resulted in the transport of 0.5 Tg of stratospheric ozone to the troposphere during the 7.5 day study period. Roughly half of the SCDA particles that entered the troposphere dispersed into the upwind and downwind WCBs.