In a manner relating to or befitting an archbishop; with regard to archiepiscopal authority or position.
From 'archiepiscopal' plus the adverbial suffix '-ly,' allowing the adjective to modify verbs and indicate how something is done or carried out.
This word is basically never used because 'archiepiscopally' requires three layers of suffixes stacked on top of a Greek-Latin hybrid root—it's a perfect example of how English technical language can become so baroque that even specialists avoid it.
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