Picked up xenology from xur last week. It's only on one character? Doesn't transfer to other characters. Quests like chaperone and blast from the past don't contribute on other characters when picked up. Why are quest when picked up on all characters the same quest across the other 2 like titan or warlock when picked up?
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Because once you have done the quest why would you do it again? All exotics once completed are available to just draw another via your collections.