Nonlocal phonological interactions are often sensitive to morphological domains. Bolivian Aymara restricts the cooccurrence of plain, ejective, and aspirated stops within, but not across, morphemes. We document these restrictions in a morphologically parsed corpus of Aymara. We further present two experiments with native Aymara speakers. In the first experiment, speakers are asked to repeat nonce words that should be interpreted as monomorphemic. Speakers are more accurate at repeating nonce words that respect the nonlocal phonotactic restrictions than nonce words that violate them. In a second experiment, some nonce words are interpetable as morphologically complex, while others suggest a monomorphemic parse. Speakers show a sensitivity to this difference, and repeat the words more accurately when they can be interpreted as having a morpheme boundary between two consonants that tend to not cooccur inside a morpheme. Finally, we develop a computational model that induces nonlocal representations from the baseline grammar. The model posits projections when it notices that certain segments often cooccur when separated by a morpheme boundary. The model generates a full Maximum Entropy phonotactic grammar, which makes distinctions between attested and rare/unattested sequences in a way that aligns with the speaker behavior.