επί των κεφαλών

here are some relevant lines from the 69 instances of "on the heads of" found in the Bank of English.  Most of those selected carry a metaphorical sense:  those whose heads they are are the victims of something:

     all their previous errors on the heads of the military whose advice they
 tongues of flame, which light on the heads of the apostles. They are given the
    of the heavenly city dance on the heads of the apostles, the joy of Heaven
     
pile of manure is heaped on the heads of our British farmers. First, only
   and it left a mark of shame on the heads of sports administrators that has
      States. <p> Today I call on the heads of the other nations of the
    
arap Moi is pouring abuse on the heads of his opponents as never before. 
 sort of praise normally piled on the heads of American bosses, but rarely

 
We poured our vitriolic sound on the heads of the tourists drinking coffee and
        solution can be forced on the heads of the Kashmiri people. Mr Kaufman
 
where the consequences fell `on the heads of innocent people quite powerless
  
real shame should be heaped on the heads of the Sunderland police. Mr Liszka
  the effects of the situation on the heads of those in the society. Until you   
 
half-naked, dropping rubbish on the heads of those who passed underneath.
    if it might bring bad luck on the heads of those who will work or live
If the punishment had fastened on the heads of the guilty, it would not be
 bright day and the sun played on the heads of the children as they entered the  
     had heaped personal abuse on the heads of two future prime ministers -
 
the microphones, calling down on the heads of his enemies the terrible maxims
    
denunciations were heaped on the heads of his English disciples,
coals of fire should be heaped on the heads of contributors who reveal their

The ILSP corpus provides two examples in this sense:

 τραγιάσκες, καβουράκια, μπερέ, ακόμη και σκούφιες αεροπόρων παρελαύνουν επί κεφαλών δικαίων και αδίκων, σαν να πρόκειται περί πραγματικής μανίας.

Τώρα το άδικο επί των κεφαλών τους και επί των κεφαλών των παιδιών τους.

επί των κεφαλών is used only in a metaphorical sense.  compare πάνω από τα κεφάλια, which can be both literal, and, as in these examples, metaphorical:

η πυρηνική απειλή παραμένει πάνω από τα κεφάλια μας
                  η τρομάρα πάνω από τα κεφάλια μας δεν έλεγε να φύγει
      
Ένα ελικόπτερο πετάει πάνω από τα κεφάλια μας

In the metaphorical examples here, note we are talking about a state (παραμένει) rather than an action (as in the English examples above). In this case, over our heads would be appropriate English.  In the last example, which is literal, we might rather expect overhead

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