Is there a way to query and find out which package(s) deliver a given file?

In a Redhat-based distro yum would come in handy with:
yum provides /path/to/file

But as far as on Debian-based (Maemo) I'm not aware of such functionality from apt.

Further investigation reveals that dpkg has limited functionality in this area:

# dpkg-query -S /path/to/file

will tell you, however dpkg-query ONLY applies to installed files (this in fact what you asked), however it should be noted that yum provides will tell you the package name (and more detailed information) even if the package isn't installed.

Additionally both of these commands support wildcards.

There is apt-file for this task.
Apt-file does however has its own database, refreshed with apt-file update. Before you install it you may want to investigate, if the application is optified to not waste space in rootfs.