We consider the decentralized provision of a global public good with local externalities in a spatially explicit model. Communities decide on the location of a facility that benefits everyone but exhibits costs to the host and its neighbors. They share the costs through transfers. We examine cooperative games associated with this so-called Not In My Back-Yard problem. We derive and discuss conditions for core solutions to exist. These conditions are driven by the temptation to exclude groups of neighbors at any potential location. We illustrate the results in different spatial settings. These results clarify how property rights can affect cooperation and shed further light on a limitation of the Coase theorem.