Google is also leasing office space on Pier 57, a commercial hub on the Hudson River. As part of that move, Google said it would pay for the construction of a ferry dock for water taxis or a cross-Hudson ferry.

Google workers have generally fit right in. They are typically young and educated and well paid. They favor jeans, shirt and no tie. They pack the Starbucks on the ground floor of the Eighth Avenue building. They browse at the T-Mobile store next door. The morning a new Android phone with a Google operating system was released, a Google employee was waiting by the door to snap up the first one, a T-mobile sales associate said.

In recent years, Google’s growing empire has started to attract the attention of its neighbors — some of whom point out that the company has not contributed as much as it could, given its extraordinary wealth and status.

“They would be much more welcome in this community if they would do their part,” said Pamela Wolff, 83, a Chelsea resident who struggled to name a big-ticket Google project for the entire neighborhood. “I think any business that comes in with such a huge footprint should be offering more.”

Google’s largess, for the most part, has been directed to specific groups and organizations. It outfitted a youth technology center with new laptops, smartboards and a music studio. Google employees have taught computer science in after-school and summer programs and have helped older immigrants learn to use Google translate.

After the email system kept crashing at Hudson Guild, a nonprofit that offers social services, a Google team was dispatched to upgrade it for free. When the Guild needed a meeting place for its 175 employees, Google supplied an auditorium, as well as breakfast and lunch. It again lent space — and some glamour — for the Guild’s “friend-raiser” for potential donors.

“Who doesn’t want to go to the Google office?” said Ken Jockers, the Guild’s executive director. “I think they are an engaged and thoughtful neighbor.”