Ravi Shankar, the Grammy Award-winning Indian sitar virtuoso who became the world’s leading representative of South Asian music, exerted a major influence on popular music in the 1960s and was the father of the jazz-pop musician Norah Jones, died Dec. 11 at a hospital near his home in Encinitas, Calif.

The musician had undergone heart valve replacement surgery last week, his family said. He was 92.

Mr. Shankar, who began his performing career as a young dancer, toured extensively as a musician after learning sitar from one of India’s great musicians. The skill with which he played the traditional Indian stringed instrument inspired several pop and rock bands in the 1960s to incorporate the sitar, most notably the Beatles with its songs “Norwegian Wood” and “Within You, Without You.”

Mr. Shankar took his music to the stages of Carnegie Hall in New York and the Kennedy Center in Washington. The London and New York philharmonic orchestras performed his concerto compositions for sitar and orchestra. During the height of the countercultural music revolution of the 1960s, he also was in the lineups at the Woodstock music festival in Upstate New York and the Monterey Pop Festival in California.

In 1971, Mr. Shankar and Beatles guitarist George Harrison organized and played at a fundraising concert to aid the war and famine victims of Bangladesh, giving birth to the modern megastar benefit concert.

Besides Harrison, who was his best-known disciple, Mr. Shankar’s musical collaborators over the years included jazz saxophonist John Coltrane, composer Philip Glass, cellist Mstislav Rostropovich and flutist Jean-Pierre Rampal. He composed music for film, radio and stage, including the score for Richard Attenborough’s movie “Gandhi” (1982) and director Satyajit Ray’s acclaimed “Apu Trilogy” in the 1950s.

Mr. Shankar’s association with the Beatles made him a household name in the West and created “an avalanche of such experiments in the rock and pop world,” South Asian music authority Gerry Farrell once wrote. But first and foremost, Mr. Shankar remained an Indian classical musician who kept the core aesthetics of his ancient art intact in the face of social, artistic and commercial shifts during the 20th century.

One reason Mr. Shankar’s music had such influence over audiences and musicians was the otherworldly quality of its tones and rhythms; the sitar produces more tones than a guitar and is based on a different theory of music. He became appalled at how this aspect of Indian music was integrated into what he called the vulgarity of rock theatrics and the association of his art with drug use.

At the 1967 Monterey Pop Festival in California, Mr. Shankar refused to be in the same evening’s lineup with Jimi Hendrix because of the way the rock guitarist was using his instrument. Hendrix made sexual motions on stage with his guitar and then lit it on fire as a finale.

“People went gaga for it, they loved it,” Mr. Shankar told the London Guardian in 2008. “But for me, the burning of the guitar was the greatest sacrilege possible. I just ran out of there. I told them that even if I had to pay some kind of compensation to get out of playing the festival, I just couldn’t do it.”

He added: “I was extremely unhappy about the superficiality of it all, especially the wrong information that Dr. Timothy Leary and others were propagating — that everyone in India takes drugs. It was a hodgepodge of Kama Sutra, Tantra, yoga, hash and LSD, while the true spiritual quality of our music was almost completely lost.”

Nonetheless, the spirit of Mr. Shankar's music was not lost on jazz saxophonist John Coltrane. Coltrane, who in midlife had a religious conversion that included the study of Hinduism, was fascinated by the tonal and rhythmic aspects of Indian music in general and by Mr. Shankar in particular. He even named his son Ravi after Mr. Shankar. (Ravi Coltrane became a prominent saxophonist.)

John Coltrane arranged to take lessons from Mr. Shankar, but the jazz musician died in 1967 a few weeks before he was to begin studying at Mr. Shankar’s music center in Los Angeles.

Because of the influence Mr. Shankar exerted on musicians of all styles and nationalities, George Harrison called the sitarist the “godfather of world music.” In fact Mr. Shankar was the true father of three musicians: his son Shubhendra, an Indian classical musician and painter, who died in 1992; Anoushka, who often performed duets with her father; and Norah Jones, an eight-time Grammy Award-winner best known for her composition and performances of jazzy popular songs.

Mr. Shankar himself counted three Grammys among his honors. His album “West Meets East,” with violinist Yehudi Menuhin, won the 1967 award for best chamber music performance. Mr. Shankar shared the 1972 award for album of the year for “The Concert for Bangladesh,” which also featured Harrison, Bob Dylan and Eric Clapton. And Mr. Shankar’s “Full Circle: Carnegie Hall 2000” won the 2001 award for best world music album.

Robindro Shankar Chowdhury was born April 7, 1920, in Benares (now Varanasi), a northern Indian city famous for its temples to the Hindu god Vishnu and the ritual bathing of pilgrims on the banks of the Ganges River. As a young man, he changed his name to Ravi, meaning “Sun.”

At 10, he joined his brother Uday’s dance company, which achieved international recognition with its tours.

A highlight for Ravi Shankar, a movie buff, was meeting film stars Clark Gable and Joan Crawford and soaking in jazz and other forms of modern American culture. The dancers also had an extended stay in Paris, where Ravi Shankar edged himself into a cultural firmament that included Anna Pavlova, Cole Porter, Jascha Heifetz and Andres Segovia.

Mr. Shankar recalled in an interview many decades later, Mr. Shankar recalled seeing Segovia, the classical guitarist, “in concert a few times. He was our neighbor when I was a child living in Paris in 1932. He would come to our house, and I’d sit on his lap.”

During his Paris years, Mr. Shankar also met Allauddin Khan, one of India’s foremost musicians and music teachers. Mr. Shankar described Khan as having a spiritual pull that he could not shake. “Suddenly, dancing was not enough,” Mr. Shankar said, and he soon returned to India and became one of Khan's most devoted sitar pupils.

It was at this time that he began a long artistic association with Khan's son, Ali Akbar Khan, a virtuoso of the sarod, another traditional Indian stringed instrument. In 1941, Mr. Shankar married Allauddin Khan’s daughter Annapurna Devi, a musician skilled in a bass stringed instrument called the surbahar.

In the early 1950s, Menuhin heard Mr. Shankar play sitar in a private home in Delhi, and the two musicians began a friendship and a cross-cultural collaboration that was to last the rest of the century. Their album “West Meets East,” which met with immediate critical and commercial success, places Menuhin's lush violin melodic figures over and within the textures of Indian drums, drone instruments and Mr. Shankar's sitar.

The album hit the No. 1 spot on Billboard's classical music charts in 1967, and in a year when the Beatles, the Rolling Stones and other popular artists were producing some of their most popular works, it also claimed a spot on Billboard’s overall best-selling chart. Mr. Shankar and Menuhin were invited to perform before invited members of the U.N. General Assembly. At this peak of popularity, Mr. Shankar wrote a memoir, “My Music, My Life,” to which Menuhin contributed the introduction.

Although he had many collaborative performances and projects with Western musicians, they were always a matter of the Westerners celebrating Indian music, or a close variation of it. He performed with the London and New York philharmonic orchestras playing his own sitar concertos, which were compositions based on Indian rhythms and ragas rather than Western styles. Nonetheless, Mr. Shankar did find a way whereby Western audiences could more fully appreciate and enjoy Indian music.

“One single raga can be performed for two hours, three hours,” he told the Ottawa Citizen. “I knew that was the big reason a Western audience couldn’t take it. It was too new, too long. I didn’t jazzify it or anything, but I edited it, didn’t beat around the bush. That was a bit shocking for our traditionalists in the beginning.”

Mr. Shankar had a notoriously complicated private life. His marriage to Annapurna Devi ended in divorce and strained his relationship with her family. He entered into a relationship with dancer Kamala Shastri that lasted from the late 1960s to early 1980s, and he began an affair with the married Sukanya Rajan, who played the tanpura at his concerts and was 31 years his junior.

In the course of his touring, Mr. Shankar also began a relationship with concert promoter Sue Jones, and the couple, in 1979, had a daughter, Geethali Nora Jones Shankar, better known as Norah Jones. Mr. Shankar had little role in raising his daughter, who failed to thank her father when she won multiple Grammys for “Come Away With Me” in 2003. They were reported to have reconciled in later years.

Mr. Shankar and Rajan, who also had a daughter, Anoushka, married in 1989. In later years, Mr. Shankar embarked on a performing and recording career with Anoushka, who became a classical Indian musician.

Survivors include his wife; two daughters; three grandchildren; and four great-grandchildren.

Speaking of his legacy a few years ago, Mr. Shankar said he was proudest of having helped expand the public notion of what Indian raga music could be. “There is so much more — erotic, romantic, sad, spiritual,” he told the publication the World and I. “One good thing is the people getting stoned don’t do that with my music anymore. I worked hard for that and achieved it.”