Plays many key roles by phosphorylating several proteins including the viral DNA processivity factor BMRF1, EBNA1 or EBNA2. Modifies the host nuclear envelope structure and induces the redistribution of nuclear envelope-associated proteins by phosphorylating host nucleoporins. Subsequently, promotes the nuclear transport of EBV lytic proteins. Required for efficient lytic DNA replication and release of nucleocapsids from the nucleus. Contributes to the compaction of host cell chromatin in cells undergoing lytic replication, presumably by phosphorylating the host condensin complex and host TOP2A. Induces disassembly of the nuclear lamina by phosphorylating with host LMNA. Phosphorylates substrates involved in capsid assembly and DNA packaging. Facilitates the switch from latent to lytic DNA replication by down-regulating EBNA1 replication function. Phosphorylates the viral immediate-early protein BZLF1 and inhibits its sumoylation by interacting with host SUMO1 and SUMO2. Phosphorylates also host SAMHD1 and thereby counteracts its antiviral effect by reducing its dNTP hydrolase activity. ATP + L-seryl-[protein] = ADP + H(+) + O-phospho-L-seryl-[protein] ATP + L-threonyl-[protein] = ADP + H(+) + O-phospho-L-threonyl-[protein] Interacts with host NUP62 and NUP153; this interaction plays a role in nuclear targeting of BGLF4. Interacts with host SUMO1 and SUMO2. the protein is present at discrete sites in nuclei, called replication compartments where viral DNA replication occurs. Belongs to the protein kinase superfamily. Ser/Thr protein kinase family.