Question: Say a group of people vote for a leader in an election but the leader then goes on to "*speak for the people*" but actually he's speaking for himself and his cronies. I'd like it to be clearly in a derogatory sense.

> 
> "Mr ..... claimed he was speaking on behalf of the people who voted for him but he was actually **[stealing]** their voice"
> 
> 
> 

What word would best fit here?

Answer: 
The most suitable word for my context was "Highjack" bringing strong, explicit implication of stealing for their own purposes. The word was contributed in a comment that was subsequently removed. Thanks to that unknown contributor!
How about 'Garble'?
According to M-W

* Garble:
 a : to so alter or distort as to create a wrong impression or change the meaning
* *garble* a story
* the candidate complained that his views had been deliberately *garbled* by his opponent

'Misrepresent' also works though.