Cladding a concrete wall with Corten steel

You can also clearly overcoat the Corten steel, then it won't weep. Of course, you have to create the desired patina beforehand. I would be skeptical that an adhesive bond would hold well. Why not hang it up? Alternatively, there are facade panels like Alucobond, which are certainly available in the desired appearance, but it's "fake".

Bonding is not a problem, I would look at Sika. However, it would not be my first choice. I would simply screw it together. Good point about discoloration. The appearance suffers from coating, and fake is a matter of taste; I don't like the discrepancy between feel and appearance.