We have a lot of deleted users in our system, so we have many "tasks to be completed" assigned to users that no more exists (deleted users).
I would give to a particular user the ability to
1) execute the "Complete Task" action (the function run by clicking on the button "Complate task" in the work item details mask).
2) Reassign task.
3) Delete task.
Do anyone knows how to grant these action to a user?
I believe OOTB those kinds of actions are restricted to Org and Site administrators, and you may not want to give that level of access to another user. A couple of other options:
1) If you haven't fully deleted a particular departed user, bring them up in the Participant Administrator, edit their password, log in as them and reassign all of their work to their replacement, and also set their Delegate function indefinitely to the replacement.
2) If the departed user is still in a Context Team use the Replace function to swap them for the new user which should also swap them on the team snapshot copies of all active workflows in that context.
Usually you can't delete tasks without terminating the host workflow that spawned it, so you may need to go that route.
In the long run consider automating this situation i.e. The deleted user running WF task can automatically be re-assigned to context owner or relevant people/ Group/Role based on business process. It's a small customization, the event manager can listen to user deletion event and can run this background task.
My question is about to give to a normal user (not an admin user) the ability to execute or reassign or delete tasks assigned to deleted user. Generally these users was deleted from a long time and the event is no more in the event manager.
Could you give me more details about your "small customization"?
The customization I mentioned about is the future way of handling the user workflow task not to the existing WF task of those deleted users. For example if a user is undergoing deletion in windchill your code can listen to this delete event and can run the program which can re-assign his task to target person.