In this paper, we explore some previously unanalysed interactions between verbal aktionsart and prepositional complementation in Norwegian, namely the alternations between a DP object and PP complements with <em>på</em> ‘on/at’ and <em>til</em> ‘to/at’. We argue that a simple account based on [±telic] or [±quantized] features cannot be correct. Instead, we generalize the notion of path and homomorphism, and integrate it in a syntactic theory of how complex events are built up compositionally. The path structure introduced by the PP interacts with the path structure of the VP to produce complex events based on ‘homomorphic unity’ in much the same way as has been argued for in the Verb + Nominal domain (Krifka 1992). Specifically, an extended location (a <em>på</em>-PP) in the complement of and activity verb (in our terms, a process subevental projection) gives rise to a non-directed path for the event; a point location ( a <em>til</em>-PP) in the complement of an accomplishment verb (one which in our terms will contain a result subevental projection) gives rise to the specification of an endpoint.