Virus?

This morning my phone downloaded a dodgy looking apk by itself. I deleted it but shortly I had a "has stopped" message for a process called something downloader.

I don't know if it's connected but now I can't get into gmail and keep getting "gmail has stopped" and "gapps has stopped" messages.

Anyone had a similar problem?

I searched a bit and found a suggestion to delete the Google account and put it back but that hasn't done it.