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The children of a heading at point can be sorted alphabetically with C-c ^ a. Can this sorting method be customized? What I want is to sort Greek words according to their Latin translitteration. For instance, I want κατά to be sorted as if it were 'kata'.

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According to org-sort-entries docstring:

(org-sort-entries &optional WITH-CASE SORTING-TYPE GETKEY-FUNC COMPARE-FUNC PROPERTY)

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The command prompts for the sorting type unless it has been given to the function through the SORTING-TYPE argument, which needs to be a character, (?n ?N ?a ?A ?t ?T ?s ?S ?d ?D ?p ?P ?o ?O ?r ?R ?f ?F ?k ?K). Here is the precise meaning of each character:

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If the SORTING-TYPE is ?f or ?F, then GETKEY-FUNC specifies a function to be called with point at the beginning of the record. It must return either a string or a number that should serve as the sorting key for that record.

So it seems you could use ?f as SORTING-TYPE and give as GETKEY-FUNC a function returning the latin transliteration of its greek word argument.

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