Crossword Genius

Investigating characters without any invite, suspiciously - they're putting it on (7)

Ross

I believe the answer is:

staging

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

'investigating characters' is the definition.
The answer and definition can be both to do with communicating as well as being present participle verbs.
Maybe they are linked in a way I don't understand?

'without any invite suspiciously they're putting it on' is the wordplay.
I cannot really understand how this works, but
'it' could be 'tag' (playground catching game) and 'tag' is found in the answer.
The remaining letters 'sing' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for staging that I've seen before include "in the greenhouse" , "Putting on (a play)" , "Putting on a show" , "Mounting (a play)" .)

I've seen this clue in The Irish Times.
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