I once had a discussion with an employee of mine who disputed the idea that people “owned” their tasks.  I disagreed, believing that people should be responsible for the success or failure of their jobs.  Recently though a much better word has come to my attention, which I believe more accurately portrays the relationship between the worker and the work, which is “stewardship.”
Here is the definition from dictionary.com:

These definitions are fine, but what I think stewardship conveys is being responsible for the success or failure of something that someone else owns.  The distinction being that someone who owns something can destroy it primarily at their expense, a steward is not approved to destroy something because someone else actually owns it.  The owner trusted the steward to care for the item.

So an employee, a team, or really even a company are not owners of what they are working on, they are stewards, responsible for success or failure, but charged with caring on the behalf of someone else.