LIVE - UPDATE - CHRIS DORNER CORNERED In Gun Battle with Cops - 1 deputy dead

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."
 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.