I have noticed that there doesn't seem to be a way to delete messages in the Archive folder.
I wonder if that functionality could be added.
Thanks.
If you are referring to an archived PM, only an admin can delete them. You have to consider that the other side (sender/receiver) may not want it deleted. Hence, the archive. Posts in archived discussions may still be deleted by the author and/or moderators. Actually edited to say "Removed by author". 
Interesting.
This is the first site I have seen where that is the policy.
If the message is in my personal archive folder, it should not affect the sender of the message, who should have their own copy.
I have two "data export complete" messages in my inbox which I want to delete but I don't see any option.
I believe we should -at least- have the ability to delete these kind of messages.
What do you think (about that)?
Currently, the only thing you can do is archive them.
Yes, I saw that.
The funny thing is... we can invite someone (who will have immediate forum access) but we can't delete messages in our inbox.
I think those of us who are in the "member" or higher trust level, should be able to delete inbox messages.
Don't know if it's supported by the forum software so I will just put it in the "wish list".
This is a link from the Discourse forum that I was referred to that essentially repeats what @thess posted above...
If you are an admin, you can delete messages.