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The union representing thousands of Kaiser Permanente health care workers in Southern California said this week its members have voted to authorize a strike, which the union says would likely “cripple’’ the health care giant’s operations locally.

The United Nurses Associations of California/Union of Health Care Professionals said 96 percent of 18,209 participating members working at Kaiser Permanente’s Southern California hospitals and clinics voted this month in favor of authorizing the strike, if necessary.

As required by law, UNAC/UHCP must give Kaiser 10 days notice before work stoppages can begin, which the union said in a statement would be the largest strike in the country so far this year.

UNAC/UHCP says it represents nearly 21,000 Kaiser registered nurses, pharmacists, midwives, physical therapists, and other health care professionals in Southern California.

The union, which is seeking 4 percent wage increases each year through 2023, says Kaiser wants to cut wages for health care workers amid major staffing shortages.

In a statement, Arlene Peasnall, senior vice president of human resources at Kaiser Permanente, said Kaiser is continuing to work with the union’s umbrella organization, the Alliance of Health Care Unions, on reaching an agreement. Kaiser and the Alliance of Health Care Unions have been in negotiations since April.

In her statement, Peasnall said, “We ask that our employees reject a call to walk away from the patients who need them. Our priority is to continue to provide our members with high-quality, safe care. In the event of any kind of work stoppage, our facilities will be staffed by our physicians along with trained and experienced managers and contingency staff.’’

According to the union, a potential strike would affect Kaiser’s hospitals and medical centers in Anaheim; Bakersfield; Baldwin Park; Downey; Fontana; Irvine, Los Angeles; Ontario Vineyard; Panorama City; Riverside; San Diego; West Los Angeles; and Woodland Hills, as well as numerous clinics and medical office buildings throughout Southern California.