From the tasklist screen Can i assign a task to a group id rather a particular user . Once the task is created for that group , any user of that group would be able to claim that task and work. Is it possible in UI and Rest API call ?
To work in a task from the tasklist UI you must be an user and claim it to you.
Why dont you use this group in your BPMN file as Candidate Group?
This will mark the task as available only to users of that group everytime a task of this type is created, but you always will have single user resolving this task at tasklist webapp, who will have to claim it.