Crossword Genius

Take for a ride and regularly shoot across crossing (4)

Ross

I believe the answer is:

hoax

I'm a little stuck... Click here to teach me more about this clue!

'across crossing' is the definition.
The answer and definition can be both acts as well as being singular nouns.
Maybe they are linked in a way I don't understand?

'take for a ride and regularly shoot' is the wordplay.
'take for a ride' becomes 'ax' (I can't justify this - if you can you should believe this answer much more).
'and' is a charade indicator (letters next to each other).
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
The alternate letters of 'shoot' are 'ho'.
'ax' put after 'ho' is 'HOAX'.

Can you help me to learn more?

(Other definitions for hoax that I've seen before include "cod" , "Deception such as the Piltdown Man" , "A plan to deceive" , "Kid" , "A fraud or deception" .)

I've seen this clue in the Sydney Morning Herald.
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