Not sure why this is not an option. I would have probably bought more than one Ornament set (especially the Star Wars ones) if I was able to change the appearance of my exotic armor.
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Mfs acting like you can't just inspect and read what armor they are using. And if it's that serious to know, then just keep the icon the same for whatever exotic piece you're wearing. I swear people in this community come up with the dumbest reasons for why we can't have a nice thing.