An external assignment is an assignment sent by email to someone who does not sign on to the system directly. An external assignment is an instance of the Assign-External class.
The directed Web Access facility causes the system to create external assignments.
To list outstanding external assignments, select Designer Studio> Process and Rules > Tools > Work Admin > External Assignments.
I don't think that sounds like what you are looking for since directed Web Access is for access via email. You envision the external users accessing the workbasket via a web based list that isn't hosted in Pega 7? I'm pretty sure that you'd need to use something like Pega Web Mashup to accomplish this. Otherwise, you will want your users to log into Pega 7 and do their work there.
Here are couple of ways you to implement Head Less pega to Access the Cases at Front End.
1) Use IAC gadget to embedded into Front end as Work Space.
2) Design the Flow and Assignments, Then Create the Rest Services or Soap Services and Get the Case info and Pass it to front end. Then Create a another Service with Resume flow and Move the Case to from assignment to another.
We have implemented in the Same way and Succeeded in Head less project.