If you don't wish to use "cc" (as per your comment on Jon Hanna's answer it means something else in your native language) you can just use the verb to copy:
1.3 (copy something to) Send a copy of a letter or an email to (a third party)
‘I thought I'd copy to you this letter sent to the PR representative’
1.4 (copy someone in) Send someone a copy of an email that is addressed to a third party.
‘I attached the document and copied him in so he'd know it had been sent’
definitions from oxforddictionaries.com
I've also seen usage without the "to" or "in", and this is the usage I tend to use myself:
I've copied my manager as he will need to provide approval
As per Jon Hanna's second example, you can also use this parenthetically:
My manager (copied) will need to provide approval
My manager (copied in) will need to provide approval
As per MT_Head's comment you may also see "copy on", although to me it sounds more natural to use "copy in on":
I've copied my manager on this email as...
I've copied Steve in on this email because...
I would advise against including the word "carbon"; I've not seen it in common usage.