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Topological insulators constitute a new class of materials with an energy gap in the bulk and peculiar metallic states on the surface. We report on new features resulting from the bulk electronic structure, based on a comprehensive nuclear magnetic resonance (NMR) study of 77Se on Bi2Se3 and Cu0.15Bi2Se3 single crystals. First, we find two resonance lines and show that they originate from the two inequivalent Se lattice sites. Second, we observe unusual field-independent linewidths and attribute them to an unexpectedly strong internuclear coupling mediated by bulk electrons. In order to support this interpretation, we present a model calculation of the indirect internuclear coupling and show that the Bloembergen-Rowland coupling is much stronger than the Ruderman-Kittel-Kasuya-Yosida coupling. Our results call for a revision of earlier NMR studies and add information concerning the bulk electronic properties. [ABSTRACT FROM AUTHOR]