Learn English – Idiom/phrase which means “to pretend not to understand or know”

Sometimes (well, often) people pretend not to understand what's going on (or pretend not to understand what the other person means, etc.) when in fact they do perfectly well.

For example, Person A is hoping that his friend Person B would let him crash at his place for a couple of days, but, so as not to appear too intrusive, he wants Person B to invite him instead of asking directly. So, he says to his friend:

Hey, Person B! I've just been kicked out of my house and I have nowhere to go. I really have to figure out where to stay the next couple of days.

Person B understands that Person A is hoping that he would offer him to stay at his place. But he chooses to pretend not to understand, and, instead of saying sorry and explaining why Person A cannot stay at his place, person B says:

There's a nice hotel near here, and it's not very expensive. I can give you the address.

Another example. Person B has secretly stolen the wallet of Person A. Person A has figured out that it was person B and when they meet, he says:

My wallet was stolen the other day.

Person B says:

Really? Oh, that's so unfortunate!

What idioms in English would one use to describe the behavior of Person B in the sample situations? I.e. pretending to be stupid or pretending not to understand something rather obvious, or pretending not to know something that you know; in other words, consciously imitating ignorance, indifference, or innocence.

In Russian, the idiom is to pretend to be a fire hose (прикидываться шлангом) or to pretend to be a boot (прикидываться валенком). The Armenian idiom is to pretend to be a donkey (իրեն էշի տեղ դնել). For me, these phrases are not quite unimaginative and cause a certain amount of amusement. I am hoping to find an English equivalent (or equivalents) that would be informal and/or sound funny(-ish), but that's not essential.

Naturally, I tried to look up the translation in the dictionary before asking, but to no avail, presumably because the phrases mentioned above are rather informal.