Christopher Dorner -- CORNERED In Gun Battle with Cops

5:15 PM PT -- The cabin has burned to the ground. Police are still surrounding the property and waiting to move in to begin searching for any sign of Dorner.

4:18 PM PT -- The entire cabin is on fire -- and one person on the scene says it's "completely engulfed in flames." It's unclear if Dorner is still inside.

3:50 PM PT -- The L.A. Times is reporting one of the deputies shot in the crossfire has died from his injuries.

2:52 PM PT -- TMZ has learned ... the L.A. City Fire Dept. is airlifting the L.A.P.D. SWAT team to Big Bear so they can help with the standoff.

2:39 PM PT -- The FAA has implemented "Temporary Flight Restrictions" around Big Bear due to the gun battle. Only law enforcement aircraft can fly in the restricted area.

The restricted area is 5 miles in radius, from the ground up to 13,000 feet above sea level, which is about 5,000 feet above ground level.

1:48 PM PT -- There seems to be a lull in the gunfire. Cops have also confirmed two deputies were shot by the suspect -- the extent of their injuries is unclear.

1:35 PM PT -- Cops involved in the gun battle are screaming at a local reporter at the scene to "get the f**k out."

Cops have repeatedly cussed at the reporter -- demanding that he leave for his own good.

Murder suspect/ex-cop Christopher Dorner is now cornered by cops in a remote cabin in Big Bear, CA ... law enforcement sources tell TMZ ... and we're now told Dorner is using smoke grenades to fend off police.

We're also hearing there are 2 officers down.

One source directly involved in the case tells TMZ, "We have him cornered." This comes after a couple were the victims of a home invasion robbery in Big Bear. The suspect fled in a white Dodge pickup truck and a State Fish and Game ranger fired on the vehicle.