They expect to be invited
Here, this sentence is a passive voice. What is the active voice of it. If it haven't then give reasons please.
The sentence you give is in the active voice.
The passive version of the sentence could be something like:
An invitation is expected.
If you're actually talking about the passive infinitive of to be invited then a similar change could be made to the original sentence:
They expect an invitation.
Or, to assume more about the context and keep the second verb:
They expect their friends will invite them.