This paper explores the discourse of the Russia-Ukraine war to outline the dominant narrative schemas anchored in the spatial geopolitical representations of globalness and localness. It uses tools from the domains of critical cognitive discourse studies and narrative research (alternative futures, discourse scenarios, deictic space, proximization) to distinguish between two most salient schemas: the Global Conflict Schema GCS narrative and the Local Conflict Schema LCS narrative. The GCS narrative conceptualizes the Russia-Ukraine war as a growing international conflict, producing serious political, economic and material consequences for the global community. GCS uses coercive rhetoric to call for immediate measures to support Ukraine so the war can be stopped before spreading beyond its current borders. The principal narrator of GCS is Ukraine, though the narrative is recontextualized in other countries located in geographical proximity to the conflict. The LCS narrative, performed mostly by the Kremlin, construes the war as a local conflict providing no reasons for foreign intervention. LCS is distinctive for its large number of sub-narratives appropriated for different geopolitical audiences, which include the Russian and Ukrainian people, and different audience groups in the West and the Global South. The latter groups re-contextualize the LCS narrative, focusing primarily on economic issues.