Q:

How to glue a map onto a globe?

I'm making a globe of Mars. I've obtained a "sliced" map of Mars that I will print. Then I'll need to cut the slices and glue them onto the globe of Earth.

The slices won't align perfectly; I can pinch or stretch each a little bit (they do have a bit of overlap) but I don't want to have the last connection off by too much - and my errors will accumulate if I just progress around the globe. How can I avoid it? A glue that allows sliding them around? Some kind of 'hint grid' for pasting them?
They are still somewhat wide; won't align with the spherical surface perfectly. A hint to make the paper more stretchy, or some other medium than paper? or some other tricks to avoid wrinkling along the edges?
How to finish it? Protect the print from dust and environment. Some kind of lacquer?

A:

I hope the surface that you're sticking them on, is smooth and not absorbing all the glue.
In that case, I'd do it the same way as applying wallpaper.
- paper that is wet, is a bit stretchy, so it can follow the curves a bit.
- wallpaper glue doesn't 'set' immediately, you can still move the pieces around for a while, this allows for better manipulation.
- where parts of the map overlap, you could glue them overlapping, take a very sharp knife and cut through the two layers of paper. Be sure not to cut through the surface underneath (though a shallow scratch should not be a problem).

A:

Since you haven't yet printed the map, I can still make my suggestion: have you thought of printing it onto fabric, instead of paper?  Fabric, depending on what type you choose, has a certain amount of stretch, and is far less likely to tear when wet and being handled, than paper.  I wouldn't go so far as to print it onto a knit fabric, but perhaps a lightweight woven cotton.  It would likely involve quite a bit experimentation before committing, but fabric for a craft such as this should not be expensive.
There are tutorials all over the internet on this.  Here is one over at Instructables. 
Good luck, sounds like a very cool project!

