This may be another case of me being behind the rest of society, but I'm now in Book 2 of Kage Baker's Company novels, Sky Coyote.
I think it's best to explain the premise of these before getting deep into the plot. Basically, in the 24th century, Zeus Inc discovers time travel. And the numerous complications with it. You can only go back in time and you can only return to the present that you left. You can take stuff back in time, but not bring things back from the past. You can't change recorded history. Which makes it rough to make a profit.
Which is why Zeus Inc changed its name to Dr. Zeus Inc, using another failed project, immortality. See, immortality can only be conveyed before the end of puberty. And it's quite expensive. Therefore the middle aged rich men who could afford it can't get it. By combining projects, Dr. Zeus sent folks back in time to make people who wouldn't be missed immortal to collect and preserve things outside of recorded history until they can be revealed in the 24th century. Dr. Zeus makes a huge profit, several beings gain immortality, everyone's happy. Well, sort of.
In Book 1, The Garden of Iden, we meet Mendoza and watch her transformation from mortal to immortal following a slight encounter with the Inquisition. Mendoza becomes a Grade 6 Botanist within the company, and gets assigned to Elizabethan England. (Ok, technically on the cups of that era. Mendoza winds up accompanying Prince Phillip's entourage to England as he prepares to marry Mary.) She falls in love with Nicholas, who has a dark past. (Heaven forbid! He was a libertine. Now he's a Lutheran in a period when Mary's trying to stamp out Anglicans and other heretical non Roman Catholic heresy.) Their love, much like two lovers in Verona a few years later, is about as successful and long lived as Mary's reign in England.
Book 2 picks up towards Winter Solstice in 1699 CE. We join Joseph the facilitator (and also the one who saved Mendoza from the loving arms of the Inquisition) as he checks in to New World One, one of The Company's outposts in South America. Wherein we find out about his past in what was to become the Basque region of the Pyrenees. However, New World One is a Mayan city with 24th century technology and humans who think the guy in charge is Kukulkan. On New Year's, said Administrator holds a fin de sicile mourning the soon to come destruction of the indigenous folks by conquistadors. On New Year's Day, 1700, Joseph and Mendoza leave for what will one day be California.
The California base is very sterile and run by 24th century mortals, who tend to view the cyborgs as something to be feared or ignored. Somehow less than human, really. All of which is a bit beside the point, since Joseph's real purpose is to save the Chumash tribe for preservation and release in the 24th century. (I might be misremembering here, but all I could think of was Buffy: the Vampire Slayer's Season 4 Thanksgiving episode when I read the tribe's name.) The Chumash religion focuses on anthropomorphic a\sky gods, of whom Sky Coyote is the one who deals with humans. The Chumash are also fairly advanced, having a sea shell based monetary system and trade with neighboring tribes, organized labor, etc. Joseph gets some prosthetic work done and takes on the role of Sky Coyote, here to save the Chumash people from the Sun's white men in big canoes who will kill the Chumash.
We have a few themes floating around in here. Neolithic Chumash society has a lot in common with late 20th Century American society, what with business versus labor concerns. The Scientists, the priests, the astronomers, and the shaman all want to argue about what Sky Coyote actually means when he says something, much the way contemporary humans debate religious dialog. Also, a tribe further south is now monotheistic, and convincing other tribes that their god is the real one, and Sky Coyote is actually a being who fell out of favor and therefore fell from grace.
Meanwhile, back at the California base, conflict is stirring between the cyborgs and the future humans. One of the more interesting passages concerns Lopez discussing how the cyborgs appreciate the culture that came before the 24th century (technically future culture at this point), versus the future humans who ignore the foundations of their culture and instead play games all day and worry about hurting abalones that the cyborgs want to eat for dinner. Also, one of the human admins would rather save the monotheistic tribe rather than the Chumash, because the monotheistic tribe's values seem to line up better with his, at least on a superficial level.
A quick look at the library catalog suggests a few more books in the series, while Wikipedia reveals the author died a while back. Which is sad, since It's really quite fascinating reading, if a bit slow in the outset.