Sustainability in computing is critical as environmental concerns rise. The cloud industry's carbon footprint is significant and rapidly growing. We show that dynamic geospatial shifting of cloud workloads to regions with lower carbon emission energy sources, particularly for more portable cloud workloads such as serverless applications, has a high potential to lower operational carbon emissions. To make the case, we build a comprehensive framework called Caribou that offloads serverless workflows across geo-distributed regions. Caribou requires no change in the application logic, nor on the provider side. It dynamically determines the best deployment plans, automatically (re-) deploys functions to appropriate regions, and redirects traffic to new endpoints. In reducing operational carbon through fine-grained, function-level offloading, Caribou does not undermine standard metrics such as performance and cost. We show how this approach can reduce the carbon footprint by an average of 22.9% to 66.6% across the North American continent. We demonstrate how a detailed specification of location constraints (e.g., to ensure compliance of one stage) can allow emission reductions for workflows (e.g., by offloading other stages). By showcasing the feasibility of carbon-aware geospatial application deployment, Caribou aims to push the boundaries of system techniques available to curtail cloud carbon emissions and provide a framework for future research.