YG Reports Over $400k in Jewelry Stolen

YG claims nearly half a million dollars in bling was taken right from under his nose -- and cops are on the case.

Law enforcement sources tell TMZ ... the rapper filed a police report Monday in L.A. for grand theft, telling police over $400,000 in personal jewelry had recently been jacked from his hotel room at the London. And, by "recently," we mean almost an entire week earlier.

We're told YG claims sometime between 11 PM on NYE and 11 AM the next morning, a briefcase containing high-priced pieces that had been placed on top of a safe was a little lighter than usual. YG told cops he noticed the missing valuables on Jan. 1 ... but for some reason, didn't get around to making an official report until 5 days later.

No suspects have been identified in the case yet ... we're told YG noted he had people coming in and out of his room that night. Makes sense -- it was a big holiday, after all.

That said, our sources say detectives will be looking into possible surveillance footage in and around the area to see if they can spot anything ... in addition to their usual investigatory methods.