Is it important for search engines to host a website in with different international providers? Let's say if I host it with just a US host provider, is it going to be hard for people located in other countries to find me?

I dont think hosting companies make a difference. Wouldnt it depend on the site, and if it can be translated and found in search engines that are used world wide. Maybe do some reaseach on which search engines has the most usage by people in other countries.

IMO always go for a hosting service which is within your region. This gives you an advantage in SERP's in your local market.

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