Large language models are deep learning models with a large number of parameters. The models made noticeable progress on a large number of tasks, and as a consequence allowing them to serve as valuable and versatile tools for a diverse range of applications. Their capabilities also offer opportunities for business process management, however, these opportunities have not yet been systematically investigated. In this paper, we address this research problem by foregrounding various management tasks of the BPM lifecycle. We investigate six research directions highlighting problems that need to be addressed when using large language models, including usage guidelines for practitioners.