Taking as an exemplar a course on Global Englishes at a Danish university, this paper debates the dares of sensitizing business communication students to the genuine or presumed connectivities that link individuals and societies. It demonstrates how language courses that center on culture and English ownership offer rich grounds on which to reposition students’ previous knowledge and observations of remote people in remote places in new formations. It is argued that the tasks and liabilities connected to cosmopolitan sensitivities' development are ethical matters shared by student and teacher.