shell variables and sed substitution

My specific goal: automatically edit a Makefile variable's (EXTRAVERSION)
value in a kernel Makefile.

So, I have a shell script that takes one parameter, a version string:

buildkernel.sh 2.6.18.21.7-custom

In the script, I assign the parameter to K_VER:

K_VER="2.6.18.21.7-custom"

I perform string operations until I get this:
XTRA_K_VER=".21.7-custom"

I export it (thinking that the proper value would be substitued when
make was run, but the variable is not expanded):
export XTRA_K_VER

So, maybe I should forget the export?

I am using the variable, XTRA_K_VER, in a substitution in a
Makefile with the idea that the variable would be expanded:

sed -f script.sed <Makefile.old >Makefile.new

where script.sed contains the following:

s#\([[:blank:]]*EXTRAVERSION\)[[:blank:]]*=[[:blank:]]*.*#\1 = $XTRA_K_VER#

The issue I am experiencing is that I want the value of XTRA_K_VER to
be used in the Makefile as opposed to the literal variable name. I do not
have a preference whether I insert the variable form of the entity (into
the Makefile) or the literal string value of the variable.

From what I have described, is there a reasonably clean way to let the
sed script expand the value of the variable before the substitution? I
thought about re-writing the sed script dynamically upon every invocation
of the program, but that seems a bit extreme to me (and potentially
challenging for others to maintain in the future).

Thanks in advance. I really appreciate the experience of the people on this site.

Cheers,

ya know.. I think i was merely missing parens around the variable
written into the Makefile. D'oh!

That's right. Also just for the record, the "export" doesn't add anything; the variable is interpolated by Make itself before the command executes. (Export is for putting stuff in the environment, so you can e.g. modify the PATH of all the processes you run from your Makefile.)