How could an AGI affect the world without a body?
An AGI could affect the world in two broad ways: interacting with devices which are linked to the internet — including robots — and getting humans to help. How an AGI interacts with the world would be a function of its goals and how it plans to achieve them. An AGI which is running biology experiments might have some robotics that it can use, but it also might just pay some graduate students, the way a human principal investigator would, to run experiments.
But how could this pose any risks, the humans will just refuse to do dangerous things, right? Probably not. Humans can be manipulated via bribery, blackmail, threats, propaganda, and more. An AGI trying to influence the world doesn’t have to look malicious or throw up red flags. Companies automatically order products from each other all the time, and people on the internet get paid to do weird stuff all the time. How much money do you think it would take to get a guy from Craigslist to run some mystery files on his computer or mix some chemicals in his garage? Not that much, especially when any guy will do.
Broadly speaking, being able to influence humans could give an AGI a large amount of access to the world, and improvements in robotics could help with this. There will be strong economic incentives to cede more decision making power to AI systems as they become intelligent, so the future might involve lots of AIs interacting with the world in complicated ways: building factories and running biology experiments. In such a fast-moving world it may become even more difficult to understand the actions AIs are taking.