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We show how the Hopf algebra of rooted trees encodes the combinatorics ofEpstein-Glaser renormalization and coordinate space renormalization in general.In particular we prove that the Epstein-Glaser time-ordered products can beobtained from the Hopf algebra by suitable Feynman rules, mapping trees tooperator-valued distributions. Twisting the antipode with a renormalization mapformally solves the Epstein-Glaser recursion and provides local countertermsdue to the Hochschild 1-closedness of the grafting operator $B_+$.Comment: 19p, minor corrections and improvements. To appear in AH

The Hopf Algebra of Rooted Trees in Epstein-Glaser Renormalization