In my presentation, I focus on the roots of intercultural communicative competence in ordinary everyday communication. I first trace the development of models of communicative competence from Hymes (1972) to Canale & Swain (1980) and Leung (2004). Against this background, I introduce the social-constructivist "My English" condition (Kohn 2011) according to which learners acquire English by developing their own versions of it in processes of individual and collaborative creative construction. I then discuss the nature of non-native speaker English from the perspective of ownership in a globalized world of communication seemingly torn between foreign language learners’ orientation towards Standard English and the requirements of communication in English as a lingua franca (ELF). In their attempt to establish a ‘third space’ of intercultural communication, lingua franca users of English are faced with the challenge of learning to explore and trust their own non-native speaker creativity in collaborative processes of accommodation and meaning negotiation. As an illustration I use examples from an ELF corpus of critical incident discussions.