I have just started working with a team that has picked up some aspects of Scrum (two week timeboxing) but not others (the team does not currently agree to all estimates or to the number of points in a sprint, but I'll change this soon.)  The product owner is also a technical resource (scientist) with some development background.Is it appropriate to have the product owner's tasks (which mostly involve research) mixed in with the team's tasks (some of which are research and some development).
Scrum: What if the Product Owner has tasks?
scrum
Experts in Scrum are very firm in stating that the Product Owner and Scrum Master should be two different people.  However, there is no such rule excluding either from the Development Team.  Note in the Scrum Guide:Development Team SizeOptimal Development Team size is small enough to remain nimble and  large enough to complete significant work. Fewer than three  Development Team members decreases interaction and results in smaller  productivity gains. Smaller Development Teams may encounter skill  constraints during the Sprint, causing the Development Team to be  unable to deliver a potentially releasable Increment. Having more than  nine members requires too much coordination. Large Development Teams  generate too much complexity for an empirical process to manage. The  Product Owner and Scrum Master roles are not included in this count  unless they are also executing the work of the Sprint Backlog.The corollary to that last line would be that, if the Product Owner is executing the work of the Sprint Backlog, he or she is counted as a member of the Development Team.That said, do whatever works to get your work done well.