Thanks for the reply. However, I was able to resolve the problem.
As I indicated before, the RadComboBox was embedded within a templated grid pager. The grid pager uses a css class that we have created (tso_grid_pager). Because our paging buttons are implemented as anchors, this css class also has some styles for anchors, as such:
.tso_grid_pager a:link, .tso_grid_pager a:visited
border:1px solid #9aafe5;
a:hover, .tso_grid_pager a:active
border:1px solid #2b66a5;
Since the RadComboBox's arrow cell is also implemented as an anchor, and since it is within the div with css class "tso_grid_pager", it was inheriting the styles associated with the tso_grid_pager's anchors.
I was able to resolve the problem by assigning a new css class to the RadComboBox, and creating a new style to override the previously inherited style:
Hopefully, this will help others that might experience the same problem.