Does the Bitcoin Wallet support both Bitcoin and Bitcoin Cash at the same time?

[leif.karlsson]

I downloaded and have my Bitcoin wallet several months ago and have transferred my Bitcoins from Coinbase to the wallet.

In the fork last yeat we got the free Bitcoin Cash and they are now sitting also on Coinbase. I want to transfer them offline to my own computer.

1) Can I transfer Bitcoin Cash to the same wallet that I have already Bitcoins?
2) If not - how do I get the Bitcoin Cash to my computer wallet?

thanks