How does trade fragmentation affect inflationary pressures? What is the response of monetary policy needed to sustain inflation at target? To answer these questions, we develop a heterogeneous agent, open-economy model featuring imperfect international risk-sharing. The model captures both the demand and supply side effects of fragmentation. It illustrates how the impact of fragmentation on inflationary pressures and the appropriate policy response depend not only on the direct effect of higher import prices on supply but, crucially, on how aggregate demand adjusts in response to lower real incomes and productivity.