I'm wanting to make a new Hunter. If I delete the one I have now will the exotics I have unlocked but no longer actually possess still be in my collection ready for purchase on my new character? I know weapons would because they're shared across characters but can't be sure for class specific armour.
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As long as you have at least one character, your vault, collection, and inventory will still be there. These categories are account based, not character based.