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No, you do not need to own the skins to buy the caches, or to even redeem their loading screen borders. The borders will be ineffective unless you use the corresponding skin however.
IE: You use 7 cores to unlock the PROJECT Ekko border and icon. Now every time you use PROJECT Ekko, you will have a special border around your loading screen portrait, but only when you use that specific skin.
Additionally, buying all three of these special one time only caches gives you a total of three fragments to upgrade into one actual cache. These actual caches have a higher rate than normal of PROJECT skins, as well as anything "legendary" or higher.
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