I am the project manager and in AgilePM or DSDM, which is a hybrid of all agile processes and methods, there is a clearly defined role for a PM.
We cannot be completely agile in our current project because there are some processes that must be done sequentially. therefore we follow a hybrid approach and quicken the pace where-ever possible. This is how we incorporated agile practices to run a Hybrid project.
We had an epic, which we broke down into user stories
We further broke down user stories into tasks
We then had two-week iterations where we were tracking the progress of tasks to completion.
We included key documentation in each iteration and where a document was incomplete at the end of an iteration, we simply put it into the next iteration. Therefore we were flexible with the end date of documentation, as long as we were able to complete the tasks within the iteration.
Finally, when the epic was ready for operational handover after the last iteration, we ensured that all related documentation was in a final version, signed off by the product owner.
We did Iteration Planning, Daily Standups, Iteration Review and Retrospective within Each iteration.
Yes, I manage budgets, I do my weekly and monthly Steering committee reporting, But I also ensure that there are daily stand-ups and iterations and there is a designated Product owner that I can approach for each epic.
You can still achieve the goals of the epic of producing a working product of value to the end-user / customer after each iteration and you can still manage your project management and governance aspects by letting the dev team what it does best, develop software, while you concentrate on getting the project governance into shape.