Yes, you can do that. Here's a simple example:

my @strings = (
    'abBbBBbb',
    'AbBbBBbb',
);

foreach my $string ( @strings ) {
    if( $string =~ m/(?-i:a)b+/i ) {
        print "$string matched.\n";
    } else {
        print "$string didn't match\n";
    }
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In particular, the (?flags:PATTERN) construct as documented in perlre is what you're after. To turn on case sensitivity for a submatch where it's off in a broader scope you would say (?i:PATTERN), and to turn it off for a submatch (where it's on in a broader scope) you would say (?-i:PATTERN).