Legal Question in Criminal Law in California

Cops can lie anytime they want to. But you do not have to speak to them and should not speak to them under any conditions. You can assume that they do not have a case against you and they want to speak to you to get information to arrest you. You should see a criminal defense lawyer immediately and let the lawyer do the talking.

There are generally two types of warrants: arrest warrants, and search warrants. What you don't explain is whether you allowed the police to search your home with the claim that they had a warrant, which I presume was claimed to be a search warrant. The failure to have a warrant for a search would generally render such search invalid. You have the right to refuse to answer police questioning, or even to request that your lawyer be present during questioning. That issue, however, is different than the warrant issue.

The police can lie in most situations, but there are limits. You have not provided enough facts to say whether they acted improperly in your case. You may want to re-post your question with some more details about what happened.