Crossword Genius

Avoided having erroneous beliefs, losing head (6)

Ross

I believe the answer is:

eluded

'avoided' is the definition.
(eluding is a kind of avoiding)

'having erroneous beliefs losing head' is the wordplay.
'having erroneous beliefs' becomes 'deluded' (believing something false).
'losing head' means to remove the first letter.
'deluded' with its initial letter removed is 'ELUDED'.

(Other definitions for eluded that I've seen before include "Evaded" , "Escaped by stratagem" , "Escaped skilfully from, avoided" , "'Dodged, escaped (6)'" , "Dodged, avoided" .)

I've seen this clue in The Guardian.
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