PIC
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Not yet sure what to do with it. It's unfortunately right behind the window, and I don't really want the waspy visitors inside. I hope they don't plan on building too much more either.
Looks like carpenter bee to me, not wasp.
Hm, you're right, doesn't look like a wasp. The color of the nest is not gray either but rather seems it has a yellowish brown. (It's all sealed up now. Quite amazing actually.)
[After looking at pictures, I don't think it's a carpenter bee though. The tail is fuzzy and striped in black and muted yellow.]