For over 6 months now on Xbox One, I've not been able to turn in Synthweave bounties. It will give you the option to turn it in but it doesn't actually turn it in. You keep the same amount no matter what. As there's a big deal made about the "fashion" aspect; this would be important. If it doesn't get fixed, I won't be able to unlock any other armor transmogs which would suck! I thought maybe this was a known issue but I've looked over the pages of recent support tickets and I've not seen it listed. Please look into this!
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Can you open your character menu, go to the sub-menu where your sparrow/ship/emblem etc are, select 'Appearance Customization' on the top right, and see if you have '15' next to your classes Synthweave material at the top. If you have 15, you're at the cap and cannot deposit anymore material into the loom until you unlock some ornaments.