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Background
Three times during the campaign, when you enter
Undergate you'll meet a woman named Omadon who will say cryptic things to you. The third meeting will come after you've completed the quest
Hunt for a Token. At that point, Omadon will ask you to speak your name "into the reflection" so that you can enter the Temple of the Faceless and hear a proposal. This last meeting will trigger the quest.
Walkthrough
To enter the Temple of the Faceless, you'll need to go to the strange mirror in the southern part of Undergate (#1) and speak your name to it. The mirror will then teleport you to the temple. Inside the temple, you'll meet Kriox and Omadon, and they'll ask you to obtain a special cloak from Malavhan in Kajeel's (#2).
Inside Kajeel's, you'll find Malavhan standing at the bar. He'll complain about how boring Westgate is, and then he'll make you a deal. If you buy some Elder Brew for him (for 400 gp), then he'll trade you his cloak for it. Unfortunately for him, he won't get to enjoy the brew very much, as it will quickly knock him unconscious. You'll then be able to claim the cloak from his body.
Note: As far as we can tell, there isn't any difference between passing and failing the fortitude check while drinking the Elder Brew. Either way you'll end up dazed, which you'll be able to remove by resting in the bar.
When you deliver
Vander Malavhan's Cloak to Kriox and Omadon, you'll earn 1000 xp, and they'll tell you a few things about the Faceless, including that the current Faceless is afflicted with a curse, but that he "embraces his condition, drawing upon its strengths and using deception to hide its weaknesses."
When you leave the temple, you'll run into Malavhan again. He'll apologize for not properly warning you about Kriox and Omadon, and then he'll encourage you to return to the temple. When you do, you'll discover that Omadon has disappeared, and that Kriox has taken over your appearance. You'll then have two ways to respond: you can kill Kriox, or you can simply leave. You won't get any further reward either way, and you won't see the cloak again.
1 - Strange Mirror
2 - Portal to Kajeel's