If you define your "exome regions" in BED format, you can use something like intersectBed from bedtools to extract the reads from whole genome BAM file.
Another option is the tool: RefCov
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One of the example tutorials on the galaxy server is extracting exonic regions only from the human genome.
That was my thought too, but do you know of a place where such a file can be found for a whole genome, like mouse? We do exon capture only, and I've been using the probe .beds, but they are bigger than exons.
.bed files can typically be created from UCSC using the Table Browser. For mouse, you could use the Table Browser to get the regions for any number of transcript models in .bed format.
Thank you very much for the inputs!